TEXTBOOK   OF 

PHYSICAL  CHEMISTRY 


BY 


AZARIAH  T.  LINCOLN,  PH.D. 

PROFESSOR   OF    PHYSICAL   CHEMISTRY 
RENSSELAER  POLYTECHNIC  INSTITUTE 


D.  C.  HEATH  £  CO.,  PUBLISHERS 

BOSTON  NEW  YORK  CHICAGO 


Copyright,  1918,  by 
D.  C.  Heath  &  Co. 


PREFACE 

THIS  textbook  is  intended  primarily  for  the  use  of  classes 
beginning  the  subject  of  Physical  Chemistry.  In  the 
preparation  of  the  text  I  have  endeavored  to  keep  in  mind 
that  the  presentation  is  to  students  who  meet  the  subject 
matter  for  the  first  time,  and  that  they  are  to  acquire  a 
broad  foundation  for  their  subsequent  work.  As  some  time 
intervenes  between  the  elementary  courses  in  which  the 
fundamental  ideas  of  chemistry  are  presented  and  the  time 
at  which  the  work  in  Physical  Chemistry  is  given,  it  is  found 
that  a  short  review  of  these  fundamental  concepts  is  neces- 
sary in  order  to  have  the  student  properly  oriented  as  to 
the  relationship  of  his  elementary  work  and  that  which  is 
usually  incorporated  in  a  course  in  Physical  Chemistry. 
That  this  is  absolutely  necessary  is  the  experience  of  most 
teachers,  and  the  result  can  be  attained  more  quickly  by 
briefly  restating  this  fundamental  matter  in  a  form  in  which 
it  can  subsequently  be  utilized.  Hence,  there  is  given  a 
resume*  of  some  of  the  information  which  the  student  is 
assumed  to  have  in  order  to  place  him  in  a  position  to 
correlate  the  new  material  with  that  which  he  already  pos- 
sesses. 

The  order  of  topics  usually  follows  the  logical  develop- 
ment of  the  subject  matter  in  that  the  experimental  data 
are  first  presented  with  the  statement  of  the  laws,  then  the 
explanation  of  the  facts  by  the  formulation  of  the  theory. 
The  limitations  are  then  emphasized  by  presentation  of 
experimental  data  which  appear  to  be  abnormal,  with  the 
subsequent  modification  of  the  theory  to  explain  these,  and 
in  some  cases  to  show  that  the  facts  are  not  in  accord  with 

iii 


IV  PREFACE 

the  present  theories.  The  historical  setting  is  illustrated 
by  recording  after  the  names  of  the  men  who  have  been 
influential  in  developing  the  science  of  chemistry,  the  date 
at  which  each  man  was  actively  engaged  in  the  work  with 
which  his  name  is  associated.  This  chronological  sequence 
of  the  main  advances  in  chemistry  is  of  vital  importance 
in  aiding  the  student  to  acquire  a  true  perspective  of  the 
subject. 

The  subject  matter  has  been  presented  by  employing  only 
the  more  elementary  mathematics,  —  arithmetic  and  alge- 
bra, —  and  in  but  few  cases  has  use  been  made  of  higher 
mathematics.  Where  the  calculus  has  been  employed, 
practically  all  of  this  matter  has  been  incorporated  in  such 
a  way  that,  if  desired,  it  can  be  omitted  without  disturbing 
the  order  of  the  presentation  of  the  subject.  In  the  pres- 
entation it  is  recognized  that  only  by  many  numerical 
examples  can  the  principles  be  properly  illustrated  and 
emphasized.  Therefore,  there  is  incorporated  in  the  Ap- 
pendix a  large  number  of  problems,  the  data  for  which  are 
tabulated  in  such  a  way  that  the  answers  appear  as  one  of 
the  parts  of  the  tabulation.  By  not  expressing  the  con- 
ditions of  the  problem  in  words,  much  space  is  saved  and 
the  instructor  may  clothe  the  data  in  whatever  form  he 
desires. 

The  selection  of  the  subject  matter  for  a  textbook  of  this 
character  resolves  itself  into  the  process  of  exclusion,  and 
the  guiding  factors  in  making  the  selections  have  been  the 
general  information  for  the  student,  the  fundamental  char- 
acter of  the  material,  and  the  technical  importance  of  the 
facts  as  well  as  of  the  theoretical  considerations.  Special 
emphasis  has  been  placed  upon  the  equilibrium  reactions 
in  gases  with  technical  uses  as  illustrated  by  means  of  prob- 
lems. The  conception  of  phases  has  been  introduced  early 
in  the  discussion,  and  their  relation  and  utilization  in  ex- 
planation of  many  operations  has  been  emphasized,  particu- 


PREFACE  V 

larly  in  the  formulation  of  the  Phase  Rule,  with  illustrations 
of  its  industrial  importance  and  applications.  The  theories 
of  solutions  have  been  presented  so  that  the  student  may 
become  familiar  with  their  experimental  basis,  the  assump- 
tions involved,  and  their  limitations.  It  is  necessary  that 
students  beginning  the  study  of  theoretical  chemistry  should 
acquire  a  working  knowledge  of  the  prevailing  theories  in 
order  to  make  the  voluminous  literature  more  accessible 
to  them.  In  order  to  accomplish  this  result  the  discussion 
has  been  extended  to  a  consideration  of  concentrated  solu- 
tions and  nonaqueous  solutions.  The  colloid  state  of  matter 
is  receiving  such  marked  attention  from  the  industrial  as 
well  as  from  the  theoretical  point  of  view,  that  it  is  be- 
coming of  great  importance.  Hence,  colloid  chemistry  has 
been  presented  in  considerable  detail. 

There  have  been  presented  a  large  number  of  tables  of  ex- 
perimental data,  most  of  which  have  been  taken  from  Lan- 
dolt,  Bornstein,  and  Roth's  Tabellen,  edition  of  1912.  With 
this  material  directly  before  the  student,  the  discussion  of 
the  principles  and  facts  presented  may  be  more  fully  carried 
on,  and  in  this  way  the  subject  can  be  much  better  presented 
to  the  student  and  he  will  be  in  a  better  position  to  see  the 
significance  of  the  conclusions.  Then  these  data  may  be 
utilized  as  a  valuable  source  of  material  from  which  prob- 
lems may  be  formulated. 

Free  use  has  been  made  of  the  available  literature  in  ob- 
taining the  material  for  this  text,  and  the  author  desires  to 
express  his  indebtedness  for  the  same,  and  particularly  to 
the  following,  to  which  the  student  is  referred  for  further 
details : 

Text  Books  of  Physical  Chemistry,  edited  by  Sir  William  Ramsay, 
which  include  A  System  of  Physical  Chemistry  by  W.  C.  McC.  Lewis, 
The  Phase  Rule  and  its  Applications  by  Alexander  Findlay,  Stoichiometry 
by  Sidney  Young,  Stereochemistry  by  Alfred  W.  Stewart,  Metallography 
by  Cecil  H.  Desch.  Monographs  on  Inorganic  and  Physical  Chemistry, 


VI  PREFACE 

edited  by  Alexander  Findlay ;  particularly  The  Chemistry  of  the  Radio- 
Elements  by  Frederick  Soddy,  and  Osmotic  Pressure  by  Alexander 
Findlay. 

Text  Book  of  Inorganic  Chemistry,  edited  by  J.  Newton  Friend ;  Vol.  I, 
An  Introduction  to  Modern  Inorganic  Chemistry  by  J.  Newton  Friend, 
H.  F.  V.  Little  and  W.  E.  S.  Turner;  Vol.  IV,  Aluminium  and  its  Con- 
geners, Including  the  Rare  Earth  Metals  by  H.  F.  V.  Little. 

Organic  Chemistry  for  Advanced  Students  by  Julius  B.  Cohen ;  Vol.  II, 
Handbook  of  Colloid  Chemistry  by  Wolfgang  Ostwald,  translated  by 
Martin  H.  Fischer. 

On  the  Physical  Aspect  of  Colloidal  Solutions  by  E.  F.  Burton,  Uni- 
versity of  Toronto  Studies  No.  36. 

An  Introduction  to  the  Physics  and  Chemistry  of  Colloids  by  Emil 
Hatschek. 

The  Chemistry  of  Colloids  by  W.  W.  Taylor.  Outlines  of  Chemistry 
by  H.  J.  H.  Fenton. 

For  valuable  suggestions  and  assistance,  the  author  wishes 
to  express  his  appreciation  to  Dr.  M.  A.  Hunter  for  reading 
the  manuscript;  to  Dr.  A.  M.  Greene  for  his  kindly  criti- 
cism on  the  chapter  on  Thermodynamic  Considerations; 
to  Mr.  T.  H.  Learning  for  his  most  valuable  assistance, 
particularly  in  collecting  and  verifying  the  data.  But 
especially  to  Mr.  G.  B.  Banks  the  author  wishes  to  express 
his  sincere  gratitude  and  deep  obligation  for  his  untiring 
and  painstaking  criticisms  and  for  his  efforts  to  prevent  errors 
which  would  otherwise  have  appeared.  Corrections  and 
suggestions  from  others  will  be  appreciated. 

A.  T.  LINCOLN. 
TROY,  N.Y. 
May,  1918. 


CONTENTS 

CHAPTER 

I.  INTRODUCTION     .        .        .        ..'.",, 

II.  LAWS  OF  COMBINATION  AND  CHEMICAL  UNITS.     =   . 

III.  THE  GAS  LAW   .        .        .      ^..  ^   \,      .  .        .     ;  . 

IV.  DETERMINATION     OF     MOLECULAR     AND     SYMBOL 

WEIGHTS      .        .        .        •    ..- ;t        »r.  ..*        . 

V.  ATOMIC  AND  MOLECULAR  THEORIES  .        .        .        , 

VI.  DEVIATIONS  FROM  THE  GAS  LAW  AND  DISSOCIATION 

OF  GASES     .        .        .        .        .        .        .        . 

VII.  THE  PERIODIC  SYSTEM       .        .        .        .        .        . 

VIII.  THE  KINETIC  THEORY  OF  GASES      .        .        .        . 

IX.  SPECIFIC  HEAT  OF  GASES  .        .        , 

X.  VAN  DER  WAALS'  EQUATION      .        .        ,        .        % 

XI.  THE  PHYSICAL  PROPERTIES  OF  LIQUIDS    .        .        . 

XII.  REFRACTION  OF  LIGHT 

XIII.  OPTICAL  ROTATION 

XIV.  SOLUTIONS 

XV.  SOLUTION  OF  LIQUIDS  IN  LIQUIDS  —  I       .        .     •    . 

XVI.  SOLUTION  OF  LIQUIDS  IN  LIQUIDS — II     . 

XVII.  PHASE  RULE 

XVIII.  SOLUTION  OF  SOLIDS  IN  LIQUIDS — I 

XIX.  SOLUTION  OF  SOLIDS  IN  LIQUIDS  —  II 

XX.  SOLUTION  OF  SOLIDS  IN  LIQUIDS — 'III      . 

XXI.  SOLUTION  OF  SOLIDS  IN  LIQUIDS  —  IV 

XXII.  APPLICATION  OF  THE  PHASE  RULE    .... 

XXIII.  OSMOTIC  PRESSURE 

XXIV.  LOWERING  OF  VAPOR  PRESSURE        .... 
XXV.  FREEZING  POINTS  AND  BOILING  POINTS  OF  SOLUTIONS 

XXVI,  THERMODYNAMIC  CONSIDERATIONS 

vii 


PAGE 
I 

6 

18 

29 
36 

46 
64 
82 
90 

97 
in 

122 

133 
I46 

157 

1 68 
183 
195 
204 
216 
229 
248 

255 
265 
273 
282 


Vlll 


CONTENTS 


CHAPTER  PAGE 

XXVII.    ELECTRICAL  CONDUCTANCE 301 

XXVIII.     ELECTROLYTIC  DISSOCIATION 321 

XXIX.    EQUILIBRIUM  BETWEEN  THE  DISSOCIATED  AND  UN- 
DISSOCIATED    PARTS    OF    AN    ELECTROLYTE    IN 

SOLUTION     .       ,-.,.       .        ;        .        .        .        .  336 

XXX.    CONCENTRATED  SOLUTIONS 358 

XXXI.    HYDRATION 368 

XXXII.    HYDROLYSIS 386 

XXXIII.    NONAQUEOUS  SOLUTIONS 395 

XXXIV.    THERMOCHEMISTRY 410 

XXXV.    COLLOID  CHEMISTRY 433 

XXXVI.    RATE  OF  CHEMICAL  REACTIONS         ....  475 

APPENDIX 507 

INDEX 541 


PHYSICAL  CHEMISTRY 


CHAPTER   I 
INTRODUCTION 

Units  of  Measure.  —  The  work  in  chemistry  and  physics 
consists  chiefly  in  making  measurements  in  order  to  ascer- 
tain the  quantity  of  the  materials  present  or  the  forces 
acting  between  these  substances.  Shortly  after  the  intro- 
duction of  the  balance  into  the  chemical  laboratory  there 
began  a  yigorous  campaign  to  determine  the  weights  of  sub- 
stances as  well  as  of  the  relative  quantities  of  the  constitu- 
ents of  which  these  were  composed  and  in  what  ratio  various 
substances  combined.  It  was  not  only  necessary  to  have 
a  unit  of  weight  but  also  a  unit  to  represent  these  combin- 
ing relations,  just  as  it  was  necessary  to  have  a  unit  of  length 
to  obtain  the  dimensions  of  substances  or  their  distances 
apart.  When  an  effort  was  made  to  measure  the  various 
forces,  some  convenient  standard  of  reference  had  to  be 
employed  in  terms  of  which  these  forces  could  be  repre- 
sented. A  unit  for  measurement  is  some  convenient  quan- 
tity of  that  particular  thing  which  is  to  be  applied  as  a  di- 
visor in  order  to  ascertain  how  many  times  this  arbitrarily 
selected  quantity  is  contained  in  the  quantity  of  the  thing 
to  be  measured.  Or  in  other  words,  a  unit  is  any  quantity 
to  which  another  quantity  of  the  same  kind  can  be  compared 
for  the  purposes  of  measurement  and  for  expressing  the 
magnitude  of  the  same.  The  measure  of  this  unit  quantity 
is  represented  by  the  number  i.  The  fundamental  units 


CHEMISTRY 

are  selected  arbitrarily,  and  the  derived  units  are  defined  in 
terms  of  the  fundamental  units. 

The  method  of  measurement  is  the  comparison  of  the 
quantity  to  be  measured  with  our  unit.  This  may  be  ac- 
complished (i)  by  applying  the  unit  directly  to  the  quantity 
to  be  measured,  as  that  of  a  foot  rule  to  a  floor  to  find  its 
dimensions,  a  graduated  vessel  to  the  liquid  to  be  measured  ; 
or  (2)  by  the  effect  the  particular  quantity  to  be  measured 
has  as  compared  to  the  effect  that  unit  quantity  has,  as  in 
determining  the  strength  of  an  alkali  by  titrating  it  against 
a  standard  acid  which  has  been  expressed  in  terms  of  our 
unit  alkali,  or  any  of  our  quantitative  methods  for  deter- 
mining the  quantity  of  a  particular  substance  present,  as 
by  determining  the  refractivity  of  a  liquid,  the  electrical 
conductance,  etc. 

The  knowledge  of  the  phenomena  occurring  about  us  has 
been  obtained  by  accurate  measurements,  and  the  funda- 
mental units  in  which  these  have  been  expressed  are  the 
units  of  time,  space,  and  mass.  The  scientific  unit  of  time, 
the  second,  is  the  86,4ooth  part  of  a  mean  solar  day,  which  is 
the  average  interval  (or  period)  that  elapses  between  suc- 
cessive transits  of  the  sun  across  the  meridian  at  any  place 
during  the  whole  year. 

Owing  to  the  fact  that  the  speed  of  the  rotation  of  the 
earth  is  decreasing,  resulting  in  the  corresponding  increase 
in  the  length  of  the  second,  it  has  been  suggested  that  the 
time  of  vibration  of  the  atom  of  some  element  be  selected 
as  our  unit  of  time,  as  this  seems  to  be  invariable  and  unal- 
terable. 

Our  conception  of  position  is  that  of  relative  positions 
only,  and  the  location  of  one  object  is  expressed  in  relation 
to  some  other  object.  The  change  of  the  position  of  a  body 
with  respect  to  another  is  termed  motion,  i.e.  motion  is 
the  change  of  position.  The  change  of  position  in  unit  time 
is  the  speed,  while  the  rate  of  change  of  position  in  a  specified 


INTRODUCTION  3 

direction  is  the  velocity.  If  this  velocity  is  not  constant 
during  successive  intervals  of  time,  the  amount  of  change 
in  the  velocity  during  the  interval  of  unit  time  is  designated 

the  acceleration,  i.e.  V2~Vl  =  a,  where  the  change  of  velocity 

has  been  from  vi  to  v2  in  the  time  /,  giving  an  acceleration 
represented  by  a. 

Matter.  —  Being  familiar  with  handling  various  sub- 
stances, such  as  iron,  sodium  chloride,  water,  etc.,  we  are 
able  to  distinguish  them  by  certain  individual  characteris- 
tics that  we  call  properties.  These  properties  are  always 
constant  and  persistent  and  are  not  detachable  from  the 
body.  The  embodiment  of  these  properties  is  that  some- 
thing which  is  familiarly  known  as  matter.  Closely  asso- 
ciated with  these  properties  are  manifestations  of  what  we 
designate  energy,  and  in  our  experiences  we  have  not  been 
able  to  separate  energy  from  matter.  Yet  it  is  through 
these  manifestations  that  we  know  of  the  existence  of  that 
which  we  designate  matter. 

The  quantity  of  matter  is  measured  by  means  of  the  bal- 
ance, and  its  measure  is  expressed  in  terms  of  weight.  This 
measure  is  the  attraction  of  the  earth  for  the  particular 
quantity  of  the  material  substance  or  matter.  Since  the 
attraction  of  the  earth  varies  with  the  distance  from  the 
center  of  the  earth,  a  body  would  not  have  the  same  weight 
on  all  parts  of  the  earth's  surface.  The  quantity  of  matter 
does  not  change,  and  the  mass,  as  it  is  termed,  remains  con- 
stant. Hence  in  stating  the  quantity  of  a  substance,  it  is 
not  sufficient  to  speak  of  its  having  a  certain  weight,  but  the 
term  mass  is  used  to  definitely  express  the  quantity  of  the 
substance.  Masses  are  compared  by  comparing  their 
weights. 

Units  of  Mass.  —  The  units  of  mass  are  founded  on  the 
kilogram,  which  is  the  metric  standard  of  mass  and  is  defined 
as  the  mass  of  a  piece  of  platinum-iridium  deposited  at  the 


4  PHYSICAL  CHEMISTRY 

International  Bureau  of  Weights  and  Measures  near  Paris. 
This  standard  of  mass,  known  as  the  International  Proto- 
type Kilogram,  is  equal  to  the  "  kilogramme  des  Archives  " 
made  by  Borda,  which  was  intended  to  have  the  same  mass 
as  a  cubic  decimeter  of  distilled  water  at  the  temperature 
of  4°  C.  and  760  mm.  Hg  pressure,  which  weighs  i  kilogram 
and  equals  actually  1.000027  cu.  dm. 

The  English  standard  of  mass  is  the  pound  and  is  the  weight 
of  a  piece  of  platinum  weighed  in  vacuo  at  the  temperature 
of  o°  C.,  and  which  is  deposited  with  the  Board  of  Trade. 

Force.  —  Force  is  that  which  changes  or  tends  to  change 
the  velocity  of  a  body.  It  may  be  measured  by  the  gravi- 
tation method,  the  ordinary  spring  balance  method,  or  the 
dynamic  method;  the  first  of  which  is  the  one  generally 
used  by  chemists.  The  unit  of  force  is  that  force  which 
produces  in  unit  mass  unit  acceleration.  In  the  C.G.S. 
system  the  unit  of  force  is  the  dyne  and  is  defined  as  that 
force  which  acting  on  a  body  of  unit  mass  produces  an 
acceleration  of  one  centimeter  per  second  per  second.  The 
unit  force  is  called  a  poundal  when  mass  is  expressed  in 
pounds,  length  in  feet,  and  time  in  seconds.  Force  may  be 
defined  by  F  —  Ma,  where  M  is  mass  and  a  is  the  accel- 
eration. 

Weight.  —  The  units  of  force,  the  dyne  and  poundal,  are 
designated  the  absolute  units,  but  the  so-called  gravitational 
units  are  more  commonly  employed,  wherein  use  is  made  of 
the  force  of  the  attraction  of  the  earth  for  the  body.  The 
unit  of  force  then  becomes  the  attraction  of  the  earth  for 
the  unit  of  mass  —  one  gram  or  one  pound. 

The  attraction  of  the  earth1  on  one  gram  causes  an 
acceleration  of  98 1  cm./sec.2.  The  force  of  one  dyne  produces 

an  acceleration  of  one  — ^when  it  acts  on  one  gram.     Hence 
sec.2 

the  weight  of  one  gram  is  equivalent  to  981  dynes. 
1  This  has  different  values  at  different  places. 


INTRODUCTION  5 

Pressure.  —  Pressure  is  a  distributed  force.  The  inten- 
sity of  pressure,  i.e.  the  pressure  per  unit  area,  is  used  ex- 
tensively in  science  ;  and  in  chemistry,  particularly,  when  the 
term  pressure  is  used  the  intensity  of  pressure  is  meant.  - 

Density  and  Specific  Gravity.  —  The  mass  of  a  substance  in 
unit  volume  is  termed  the  density  of  that  substance.  Density 

is  represented  by  p.     Then  by  definition  p  =          .      The 

specific  gravity  of  a  substance  is  the  ratio  of  the  mass  of  a 
given  volume  of  a  substance  to  the  mass  of  an  equal  volume 
of  another  substance  taken  as  a  standard.  The  specific 

gravity  is  represented  by  s.    Then  s  =  — ,  where  g  is  the  mass 

& 

of  the  substance,  and  g,  is  the  mass  of  an  equal  volume  of 
the  standard  substance.  It  is  not  always  customary  to  com- 
pare the  substance  at  the  same  temperature.  Hence  if  water 
at  its  greatest  density  (4°  C.)  is  selected  as  the  standard 
and  the  other  substance  compared  with  it  at  this  tempera- 

.0 

ture,  this  is  usually  expressed  -^ ,  while  if  the  substance  is  at 

4 
some  other  temperature,  as  20°,  the  comparison  with  water 

Q 

at  4°  would  be  indicated  as  follows  :  ^-,  and  the  expression 

4 

Q 

^  signifies  that  both  the  substance  and  the  standard  are  to 

be  compared  at  15°.     We  should  also  have  s  =  —  ,  in  which 

P» 

p  is  the  density  of  any  substance,  and  p,  is  the  density  of  the 
standard. 


CHAPTER   II 
LAWS  OF   COMBINATION  AND    CHEMICAL  UNITS 

THE  uniform  occurrence  of  natural  phenomena  is  observed 
to  take  place  and  the  conditions  best  suited  for  their  repro- 
duction are  ascertained  by  experimentation.  The  facts 
gathered  by  observation  and  experimentation  are  classified, 
and  certain  particular  groups  of  related  facts  are  then  ex- 
pressed in  a  generalization  which  is  the  so-called  law.  Or, 
as  Mellor  expresses  it,  "  The  laws  of  chemical  and  physical 
phenomena  are  collocations  of  those  circumstances  which 
have  been  found  by  experiment  and  observation  to  accom- 
pany all  chemical  and  physical  changes  included  in  the 
statement  of  the  law."  We  have  as  some  of  the  funda- 
mental generalizations  of  science  the  following :  The  Law  of 
the  Conservation  of  Energy ;  the  Law  of  the  Conservation 
of  Matter;  Newton's  Law  of  Gravitation;  Boyle's  Law; 
etc.  We  thus  see  that  a  Law  of  Science  is  a  general  statement 
of  what  has  been  found  to  be  true  by  experiment  and  observation 
and  of  what  will  probably  be  true  in  the  future. 

THE  LAW  OF  DEFINITE  PROPORTIONS 

When  magnesium  is  burned,  it  is  changed  to  the  white 
oxide,  and  we  have  on  the  one  hand  metallic  magnesium 
and  on  the  other  hand  the  white  oxide,  there  being  no 
gradation.  The  amount  of  the  magnesium  oxide  that  can 
be  formed  depends  upon  the  quantities  of  magnesium  and 
oxygen  available,  and  there  is  a  constant  relation  between 
the  amounts  of  substances  taken  and  the  amount  of  sub- 

6 


LAWS  OF  COMBINATION  AND   CHEMICAL  UNITS          7 

stance  formed.  In  general  this  may  be  stated  that  when 
substance  A  changes  to  substance  B  the  ratio  of  the  masses 
is  constant.  It  was  not  possible  to  formulate  any  such  law 
until  the  balance  was  introduced  by  Lavoisier.  It  was  then 
demonstrated  that  100  parts  of  zinc  always  yield  124.5  parts 
of  zinc  oxide.  By  using  different  amounts  of  potassium 
chloride,  varying  from  44  to  80  grams,  the  result  of  seven 
experiments  showed  that  100  parts  of  potassium  chloride 
yield  135.645  parts  of  potassium  nitrate. 

If  two  chemically  homogeneous  substances,  A  and  B, 
react  upon  each  other  and  yield  a  third  substance,  C,  then 
the  following  relations  hold  : 

Mass  A       T.  ,  AX     Mass  A       T,      Mass  B        „ 

TT7 ~  =  K  (constant) :  ^ -^  =  Ki ;    ^ -^  —  Kz. 

Mass  B  '  Mass  C  Mass  C 

This  may  be  demonstrated  by  adding,  drop  by  drop,  a 
solution  of  potassium  bromide  to  a  solution  of  silver  nitrate. 
It  has  also  been  shown  that  these  relations  hold  under  what- 
ever conditions  the  substances  react/  For  example,  the 
amount  of  silver  chloride  formed  from  a  constant  given  weight 
of  silver  is  always  the  same,  whatever  the  method  be  by 
means  of  which  it  is  prepared,  as  is  shown  by  the  following : 

1.  Burning  Ag  in  Cl  gas  100  g.  Ag  yielded  132.842  g.  AgCl. 

2.  Dissolving  Ag  in  KC1  100  g.  Ag  yielded  132.847  g.  AgCl. 

3.  Precipitating  AgNO3  with  HC1  aq  100  g.  Ag  yielded  132.848  g.  AgCl. 

4.  Precipitating  AgNO3  with  NaCl  aq  100  g.  Ag  yielded  132.842  g.  AgCl. 

A  large  number  of  experiments  were  made  to  determine 
whether  the  mass  formed  was  equal  to  the  sum  of  the  masses 
taking  part  in  the  reaction.  In  seven  experiments  with  the 
formation  of  silver  iodide  from  silver  and  iodine,  in  which 
quantities  of  silver  varying  from  27  to  136  grams  were  used, 
the  weights  of  the  silver  iodide  formed  did  not  differ  from 
the  sum  of  the  weights  of  the  silver  and  the  iodine  taken  by 
more  than  one  part  in  20,000  in  any^ase.  From  this  it  is 
seen  that  there  is  a  definite  relation  between  the  substances 


8  PHYSICAL   CHEMISTRY 

used  and  the  products  formed.  This  may  be  expressed  in 
the  following  form  :  The  ratio  of  the  mass  formed  to  the  con- 
stituents is  constant  and  also  the  ratio  of  the  constituents  to  the 
mass  formed  is  constant.  This  is  termed  the  Law  of  Definite 
or  Constant  Proportions. 

While  this  has  been  fully  demonstrated  to  the  satisfaction 
of  most  investigators,  there  are  some  who  still  question 
whether  the  mass  of  a  substance  always  remains  constant 
during  its  passage  through  chemical  changes.  Very  recently 
Landolt 1  published  the  result  of  his  investigation  on  the  ques- 
tion as  to  whether  chemical  changes  alter  the  mass  of  a 
particular  substance.  Of  14  reactions  of  various  types  only 
two  gave  systematically  a  change  in  weight  larger  than  the 
errors  of  observation.  Each  of  the  experiments,  in  which 
250  to  310  grams  were  used,  has  corresponding  differences  in 
weights,  varying  from  0.068  mg.  to  o.n  mg.  Out  of  70  ex- 
periments 6 1  showed  losses  in  weight.  Babcock,  from  his 
work  upon  the  effect  of  molecular  changes  upon  weight,  states 2 
that  his  experiments  indicate  that  the  weight  of  a  body  is  an 
inverse  function  of  its  energy.  While  the  difference  between 
the  weight  of  the  ice  and  the  water  resulting  from  it  is  always 
small,  the  ice  was  always  found  to  be  heavier  than  the  water. 

THE  LAW  OF  MULTIPLE  PROPORTIONS 

The  mass  of  a  system  is  not  altered  by  chemical  changes 
that  occur  in  the  system,  or,  as  expressed  above,  the  mass  of 
a  composite  substance  is  equal  to  the  sum  of  the  masses  of 
its  component  elements.  By  the  term  element  we  under- 
stand those  particular  substances  which  have  so  far  resisted 
all  efforts  of  the  analyst  to  decompose  them  into  simpler  or 
more  elementary  constituents.3  We  have  already  seen  that 

1  Landolt,  Jour,  de  chem.  phys.  6,  625-27  (1908). 

2  In  a  private  communication  to  the  author. 

3  The  rare  earth  elements  constitute  a  group  of  closely  related  ele- 
ments that  require  peculiar  and  special  methods  in  order  to  separate 


LAWS   OF  COMBINATION  AND   CHEMICAL  UNITS         9 

these  elements  combine  in  constant  ratios  to  form  chemically 
homogeneous  substances.  Such  chemically  homogeneous 
substances,  whose  percentage  composition  by  mass  is  in- 
variable, are  termed  chemical  compounds. 

By  burning  portions  of  10  grams  of  lead  in  oxygen  the 
following  quantities  of  lead  oxide  were  formed:  10.77, 
10.775,  10.78,  and  10.75  grams,  and  Berzelius  found  as  an 
average  of  his  determinations  10.78  grams  of  the  oxide  of 
lead  produced  from  10  grams  of  lead.  Taking  10.78  as  the 
value,  and  expressing  the  amount  of  lead  oxide  produced 
from  100  grams  of  lead,  we  would  obtain  107.8  grams  of  the 
yellow  oxide  of  lead.  It  has  also  been  found  that  100  grams 
of  lead  unite  with  11.7  grams  of  oxygen  to  form  minium 
(red  oxide  of  lead)  and  that  100  grams  of  lead  unite  with  15.6 
grams  of  oxygen  to  form  brown  oxide  (peroxide)  of  lead. 
These  different  quantities  of  oxygen  combining  with  the  same 

and  distinguish  them.  Certain  elements,  which  include  uranium,  radium, 
polonium,  actinium,  etc.,  are  designated  radioactive  elements  and  are 
characterized  by  giving  rise  to  emanations.  The  theory  of  the  disinte- 
gration of  these  radioactive  elements  assumes  that  the  emanations  give 
rise,  in  some  cases,  to  active  deposits  which  are  transformed  into  another 
element,  and  this  in  turn  is  transformed  into  a  non- radioactive  and  stable 
element.  In  some  radioactive  changes,  the  ex.  particles  emitted  are 
charged  atoms  of  helium,  as  is  illustrated  in  the  growth  of  helium  from 
actinium.  Resulting  from  these  emanations  there  is  a  group  of  elements 
of  different  atomic  weights  but  which  are  chemically  identical.  Such  a 
group  of  elements  is  termed  isotopes  and  the  elements  are  called  isotopic. 
The  following  members  of  the  actinium  series  are  given  by  Soddy :  * 

1.  Radioactinium,  thorium,  radiothorium,  ionium,  uranium-X. 

2.  Actinium  and  mesothorium-2. 

3.  Actinium-X,  radium,  mesothorium-i,  thorium-X. 

4.  Actinium  emanation  and  emanations  of  radium  and  thorium. 

5.  Actinium-B,  lead,  radium-B,  thorium-B,  radium-D. 

6.  Actinium-C,  bismuth,  radium-C,  thorium-C,  radium-E. 

7.  Actinium-D,  thallium,  and  thorium-D. 

*  Soddy,  The  Chemistry  of  the  Radio-Elements  (1914),  and  the  Text-book  of  Inorganic 
Chemistry,  Edited  by  J.  Newton  Friend,  Vol.  IV  by  H.  F.  V.  Little,  are  sources  of  additional 
information  and  extensive  references  to  the  literature. 


10  PHYSICAL   CHEMISTRY 

amount  of  lead  (100  grams)  are  in  the  ratio  of  7.8 :  11.7 : 
15.6,  which  is  the  more  simple  ratio  of  2  :  3  :  4  ;  hence  a  con- 
stant quantity  of  lead  combines  with  different  quantities  of 
oxygen  in  the  simple  integral  ratio  2:3:4.  Similarly  it  has 
been  found  that  100  grams  of  nitrogen  unite  with  the  fol- 
lowing quantities  of  oxygen  to  form  distinct  chemical  indi- 
viduals:  57.1;  114.3;  I7I-4>  228.6;  285.7  grams,  which 
reduces  to  the  following  simple  ratio  :  1:2:3:4:5.  In  the 
case  of  hydrogen  and  oxygen  the  quantities  of  oxygen  found 
in  combination  with  the  same  quantity  of  hydrogen  are  in 
the  ratio  of  1:2.  Hence  from  the  above  the  following 
general  statement  may  be  made  : 

When  an  element  combines  with  another  element  or  group  of 
elements  to  form  different  compounds,  the  masses  of  the  first 
element  that  combine  with  a  given  mass  of  the  other  element 
or  group  of  elements  are  in  some  simple  ratio  to  one  another. 

THE  LAW  OF  RECIPROCAL  PROPORTIONS 

In  the  above  examples  of  ratios  between  the  elements  lead 
and  oxygen,  we  expressed  the  amount  of  oxygen  that  com- 
bined with  100  parts  by  weight  of  lead.  We  could  have 
expressed  the  ratio  by  stating  the  amount  of  lead  that  com- 
bined with  i,  or  10,  or  100  parts  of  oxygen.  The  same  is 
true  in  the  case  of  oxygen  and  nitrogen;  either  element 
might  have  been  selected  as  the  unit  of  comparison,  in  any 
convenient  quantity.  Further,  if  the  ratio  of  the  two  ele- 
ments, nitrogen  and  oxygen,  is  established,  and  also  the  ratio 
of  hydrogen  and  oxygen,  the  ratio  of  hydrogen  and  nitro- 
gen can  readily  be  ascertained  by  calculation.  Again,  if 
the  ratio  of  hydrogen  and  chlorine  be  determined  and  the 
other  two  ratios,  nitrogen  to  oxygen  and  oxygen  to  hydro- 
gen, then  the  cross-relation  between  chlorine  and  nitrogen 
can  be  calculated.  This  relation  can  be  illustrated  in  the 
case  of  chlorine,  iodine,  and  silver.  Let  us  compare  the 
ratios  of  the  amounts  of  these  elements  that  combine  with 


LAWS  OF  COMBINATION  AND   CHEMICAL  UNITS       II 

equal  amounts  of  silver,  say  75.26  parts.  In  silver  chloride 
we  have  24.74  per  cent  chlorine  and  75.26  per  cent  silver; 
in  silver  iodide  we  have  54.04  per  cent  iodine  and  45.96  per 
cent  silver ;  in  chlorine  iodide  we  have  2 1.84  per  cent  chlorine 
and  78.16  per  cent  iodine. 
Then  from  the  proportion 

Iodine :  Silver : :  Iodine :  Silver 

we  have  54-04  :  45.96  ::  x:  75.26. 

From  which 

x  =  54"°4  X  I5'26  =  88.49 
45.96 

the  amount  of  iodine  that  would  combine  with  75.26  parts  of 
silver.  Since  24.74  parts  of  chlorine  combine  with  this  same 
amount  of  silver,  88.49  parts  of  iodine  would  be  equivalent 
to  24.74  parts  of  chlorine.  One  part  of  iodine  will  be  equiva- 
lent to  0Q  =  0.279  part  of  chlorine.  In  the  direct  com- 
88.49 

bination  of  chlorine  and  iodine  we  have  the  ratio  of  21.84 

parts  of  chlorine  :  78.16  parts  of  iodine,  or       '   .  =  0.279 

70.10 

part  of  chlorine,  uniting  with  one  part  of  iodine,  which  is 
the  same  ratio  as  above.  By  a  similar  method  these  cross- 
relations  can  be  calculated  between  all  of  the  elements,  and 
it  is  this  relation  that  is  known  as  the  Law  of  Reciprocal 
Proportions,  or  the  Law  of  Equivalents.  It  may  be  expressed 
as  follows : 

When  different  elements  are  combined  successively  with  any 
other,  or  with  a  group  of  others,  the  masses  of  the  former 
that  are  combined  with  a  given  mass  of  the  latter  are  to  one 
another  in  the  same  ratio  in  which  these  different  elements 
combine  with  any  other  element  or  group  of  elements. 

From  our  consideration  of  the  previous  laws,  and  our 
information  concerning  chemical  compounds,  it  is  evident 
that  we  have  to  distinguish  between  equal  quantities  of  the 


12  PHYSICAL   CHEMISTRY 

constituents  of  a  compound  and  equal  chemical  quantities 
of  the  constituents.  In  the  compounds  cited  above,  silver 
chloride,  for  instance,  contains  75.26  per  cent  of  silver  and 
24.74  per  cent  of  chlorine,  i.e.  these  quantities  of  silver  and 
chlorine  are  equal  chemically.  In  the  chemical  sense,  then, 
the  equal  quantities  of  matter  are  the  weights  or  masses 
which  unite  with  each  other  chemically.  The  amounts  of 
the  different  substances  that  unite  chemically  are  chemically 
equivalent  and  depend  entirely  upon  the  specific  nature  of 
the  substances. 

UNITS  OF  CHEMISTRY 

We  employ  symbols  to  represent  the  elements  and  a  com- 
bination of  symbols  in  the  form  of  a  formula  to  represent  the 
composition  of  a  compound.  For  example,  water  is  com- 
posed of  hydrogen  and  oxygen,  and  hydrogen  peroxide  is 
composed  of  hydrogen  and  oxygen.  We  use  H  to  represent 
the  element  hydrogen  and  O  to  represent  the  element  oxygen ; 
then  the  combination  HO  represents  both  water  and  hydro- 
gen peroxide,  but  not  their  composition.  By  analysis  we 
know  that  water  contains  88.85  per  cent  of  oxygen  and  11.15 
per  cent  of  hydrogen,  and  hydrogen  peroxide  5.91  per  cent 
of  hydrogen  and  94.09  per  cent  of  oxygen.  In  water  the 
ratio  is  11.15:88.85.  Then  the  amount  which  combines 
with  94.09  parts  of  oxygen  in  the  hydrogen  peroxide  would 
be  11.15:88.85:  :#:94.09.  Solving  for  x  we  have  11.82 
parts.  The  quantities  of  hydrogen  combining  with  the 
same  quantity  of  oxygen,  94.09  parts,  are  11.82  parts  and 
5.91  parts,  which  are  in  the  ratio  of  2  :  i.  That  is,  there  are 
two  different  quantities  of  hydrogen  combining  with  the 
same  quantity  of  oxygen  to  form  these  two  different  chem- 
ical substances,  water  and  hydrogen  peroxide.  The  hydro- 
gen has  two  combining  weights  or  equivalents.  We  could 
use  this  weight  of  oxygen  as  our  unit  quantity  and  represent 
it  by  the  symbol  for  oxygen,  O,  or  we  could  select  any 


LAWS   OF   COMBINATION  AND   CHEMICAL   UNITS        13 

other  quantity  arbitrarily.  The  quantity  that  has  been 
selected  arbitrarily  is  16,  and  so  we  shall  arbitrarily  select 
as  our  symbol  weight  of  oxygen,  16  grams.  Then  the  equiva- 
lent weights  of  hydrogen  would  be  2  in  the  compound  water 
and  i  in  the  compound  hydrogen  peroxide.  Then  the 
formulae  for  these  substances  could  be  written  respectively 
H2O  and  HO,  if  we  let  the  symbol  H  represent  the  smaller 
amount  of  hydrogen  combining  with  the  16  grams  of  oxy- 
gen, thus  avoiding  a  fractional  part  of  the  symbol  weight 
were  we  to  select  the  larger  value  H  =  2. 

From  34  grams  of  hydrogen  peroxide  we  can  obtain  16 
grams  of  oxygen  and  18  grams  of  water  at  the  same  time. 
This  1 8  grams  of  water  on  decomposition  will  yield  16  grams 
of  oxygen  and  2  grams  of  hydrogen ;  that  is,  the  oxygen  of 
hydrogen  peroxide  can  be  separated  into  two  equal  quantities, 
but  the  oxygen  in  the  water  cannot  be  thus  separated,  for 
we  obtain  free  hydrogen  and  free  oxygen.  From  this  we 
assume  that  the  oxygen  in  water  is  in  the  simplest  amount 
possible  and  is  the  quantity  represented  by  our  symbol 
weight  of  oxygen,  O,  while  in  the  peroxide  there  is  twice  this 
quantity,  or  O2. 

In  the  decomposition  of  hydrogen  peroxide  we  find  that 
all  of  the  hydrogen  present  remains  with  one  part  of  the 
oxygen  and  is  the  same  as  that  in  the  water.  Now  if  we 
treat  water  with  sodium,  we  obtain  free  hydrogen  and  a 
compound,  sodium  hydroxide,  which  upon  analysis  gives 
sodium,  oxygen,  and  hydrogen,  —  all  of  the  oxygen  of  the 
water  appearing  in  this  compound  and  the  hydrogen  of  the 
water  separating  into  two  equal  parts,  one  part  appearing 
free  and  the  other  in  combination  with  the  oxygen  and 
sodium.  The  formula  for  water  must  show  that  the  hydro- 
gen can  be  divided ;  therefore,  the  formula  becomes  H2O. 
vSimilarly,  the  formula  for  hydrogen  peroxide  must  show 
that  it  contains  the  same  amount  of  hydrogen  as  in  water 
and  also  that  the  oxygen  contained  can  be  divided ;  hence 


14  PHYSICAL   CHEMISTRY 

the  formula  for  hydrogen  peroxide  becomes  H2O2,  instead  of 
HO,  which  we  saw  represents  the  chemical  composition  as  well. 

A  chemical  formula  is  a  combination  of  symbols  wherein 
each  symbol  represents  that  equivalent  quantity  of  the  ele- 
ment which  we  cannot  further  divide  by  chemical  trans- 
formations. These  chemical  formulae  are  the  result  of  ex- 
periment and  are  designated  the  empirical  formulae.  If  our 
method  is  good,  only  integral  multiples  of  the  chemical  units 
represented  by  symbols  enter  into  and  go  out  of  combina- 
tion. The  symbol  weight  of  oxygen  is  defined  as  16  grams  of 
oxygen,  and  the  symbol  weight  of  hydrogen  is  then  i.  The 
sum  of  the  symbol  weights  is  designated  the  formula  weight. 
This  is  usually  called  the  molecular  weight.  For  example, 
the  formula  we  derived  for  the  water  is  H20 ;  two  symbol 
weights  of  H  =  2  and  one  of  O  =  16  and  the  sum  18  is  the 
formula  weight  for  water. 

The  symbol  weight  of  other  elements  may  be  determined 
in  a  similar  manner.  Carbon  when  burned  in  air  forms  two 
oxides  which  are  compounds  of  oxygen  and  carbon;  by 
analysis  one  contains  12  grams  of  carbon  and  the  other  6 
grams  of  carbon  in  combination  with  16  grams  of  oxygen. 
So  the  formulae  would  be  C2O  and  CO  or  CO  and  CO2  re- 
spectively, depending  upon  whether  we  select  12  or  6  as  the 
equivalent  weight  of  C.  Since  carbon  has  two  combining 
weights,  it  is  necessary  for  us  to  have  more  data  in  order  to 
decide  which  we  shall  select  as  the  symbol  weight.  Either 
of  the  formulae  would  represent  the  chemical  composition 
and  would  be  designated  an  empirical  formula. 

In  the  case  of  nitrogen,  we  have  five  different  compounds 
of  nitrogen  and  oxygen.  Expressed  in  terms  of  the  quantities 
of  nitrogen  in  combination  with  16  grams  of  oxygen,  we  have 
28,  14,  9^,  7,  5!  grams  of  nitrogen  respectively,  i.e.  we  have 
five  different  combining  weights  of  nitrogen,  and  the  ques- 
tion arises,  which  of  these  equivalent  weights  shall  be  selected 
as  the  symbol  weight  of  nitrogen  ? 


LAWS  OF  COMBINATION  AND   CHEMICAL  UNITS       15 

The  answer  to  this  question  is  obtained  by  a  consideration 
of  the  volume  relations  of  gaseous  compounds  and  of  the 
elements  entering  into  the  reactions.  These  volume  rela- 
tions are  summed  up  by  Gay  Lussac's  Law  of  Combination  by 
Volume,  which  is  stated  as  follows :  When  reacting  gaseous 
elements  combine,  the  volumes  of  the  different  gases  under  the 
same  conditions  of  pressure  and  temperature  are  in  simple 
ratio  to  one  another  and  to  the  resulting  products. 

Taking  the  volume  of  16  grams  of  oxygen  as  the  unit 
volume  under  specified  conditions  of  temperature  and 
pressure,  we  find  experimentally  under  these  same  condi- 
tions of  temperature  and  pressure  the  following  volume  re- 
lations between  the  reacting  substances  and  the  resulting 
product : 

Hydrogen      +  Oxygen  =  Water 

2  grams  16  grams  18  grams 


2. 


+     n    -;". 

+                          i  vol.                  = 

+                     Hydrogen             =     Hyc 
i  gram 

+       D     -  ;  : 

-f-                         I  vol.                  = 

+                       Oxygen               =     Niti 
1  6  grams 

*       D     - 

•+•                         i  vol.                   = 

+     Nitrous  oxide       =         Water 
44  grams                     18  grams 

1      1 

2  VOls. 

Chlorine 
35.5  grams 

2  VOls. 

Irochloric  acid 
36.5  grams 

1     1 

i  vol. 

Citric  oxide 
30  grams 

2  VOls. 

•ogen  peroxide 
46  grams 

1 

2  VOls. 

Hydrogen 
2  grams 

2  VOls. 

V      Nitrogen 
28  grams 

1 

+ 

1 

2  VOls. 

+             2  VOls.                   =            2  VOls.           +          2  VOls. 

16  PHYSICAL   CHEMISTRY 

Nitrogen        -j-  Hydrogen  =  Ammonia 

14  grams  3  grams  17  grams 


i  vol.  +  3  vols.  =  2  vols. 

In  No.  i  we  observe  that  since  16  grams  of  oxygen  is  the 
arbitrarily  selected  symbol  weight  and  the  quantity  of  hydro- 
gen represents  2  symbol  weights  of  hydrogen  the  prod- 
uct, 1 8  grams  of  water,  is  represented  by  the  formula  H2O. 
We  notice  that  the  formula  weight  of  water  occupies  twice 
the  volume  of  the  one  symbol  weight  of  oxygen,  while  two 
symbol  weights  of  hydrogen  occupy  the  same  volume  as  the 
formula  weight  of  water  or  twice  the  volume  of  one  symbol 
weight  of  oxygen.  From  an  examination  of  the  weights  of 
these  various  compounds  used  and  produced  in  these  five 
examples,  it  will  be  noticed  that  the  volume  occupied  by  the 
formula  weight  of  water  (2  vols.)  is  the  same  as  that  occupied 
by  the  formula  weights  of  the  other  compounds :  hydro- 
chloric acid,  nitric  oxide,  nitrogen  peroxide,  nitrous  oxide, 
and  ammonia.  That  is,  the  formula  weight  of  every  gaseous 
compound  considered  above  occupies  the  same  volume.  We 
can  generalize  and  state  that  the  formula  weight  of  all 
gaseous  compounds  occupies  the  same  volume  under  the 
same  conditions  of  temperature  and  pressure.  This  may  be 
the  same  as  the  empirical  formula,  which  is  taken  as  the 
simplest  formula,  or  it  may  be  some  integral  multiple  of  the 
empirical  formula. 

Experimentally,  it  has  been  found  that  16  grams  of  oxygen 
at  o°  C.  and  under  760  mm.  mercury  pressure  occupies  11.2 
liters.  Under  these  conditions  of  temperature  and  pressure 
22.4  liters  is  therefore  the  volume  occupied  by  the  formula 
weight  of  the  gaseous  compounds.  This  volume  is  termed 
the  formula  volume. 

The  formula  of  a  compound  is,  then,  a  combination  of 
symbols  that  represents  the  percentage  composition  of  the 


LAWS   OF  COMBINATION  AND   CHEMICAL  UNITS       17 

compound  and  such  that  the  formula  weight  in  grams  of  the 
compound  in  the  gaseous  state  occupies  22.4  liters  of  space 
under  standard  conditions.  A  formula  is,  therefore,  purely 
an  arbitrary  affair,  subject  to  definition.  It  follows  then 
that  we  can  have  a  formula  of  an  element ;  thus  O2  is  a  com- 
bination of  two  symbol  weights  of  oxygen  representing  32 
grams  of  oxygen  and  occupying  22.4  liters  under  standard 
conditions  of  temperature  and  pressure.  Similarly  the  for- 
mula of  hydrogen  is  H2,  of  chlorine  C^,  of  nitrogen  N2. 

Rewriting  the  above  reactions,  employing  formulae  for  the 
reacting  substances  and  products,  we  have : 

1.  2  H2   +  O2    =2H2O 

2  vols.   +  I  Vol.    =  2  vols. 

2.  C12     +    H2  =2HC1 

I  vol.   +  I  vol.    =  2  VOls. 

3.  2  NO  +    O2    =2  NO2 

2  VOls.   +   I  VOl.    =   2  VOls. 

4.  .    H2     +  N2O  =  H2O  +  N2 

i  vol.  +  I  vol.  =  I  vol.  +  i  vol. 

These  chemical  equations  represent  the  chemical  reaction 
and  the  quantities  by  weight  of  the  reacting  substances. 
The  coefficients  of  the  formulas  appearing  in  the  equation  are 
the  same  as  the  number  of  volumes  of  the  compounds  in  the 
gaseous  state. 

Experimentally,  we  have  developed  that  equal  volumes  of 
substances  in  the  gaseous  state  contain  the  same  number  of 
formula  weights  of  the  compounds.  (This  is  Avogadro's  Law.) 

We  have  also  established  the  following  rule  for  checking 
the  symbol  weight  of  an  element :  Determine  the  weights  in 
grams  of  the  designated  element  in  2  2 .4  liters,  under  standard 
conditions,  of  the  gaseous  compounds  of  that  element.  The 
greatest  common  divisor  of  all  these  numbers  is  the  symbol 
weight  of  the  element. 


CHAPTER  III 
THE   GAS  LAW 

THROUGH  whatever  chemical  change  a  substance  passes, 
the  mass  of  it  remains  the  same.  The  same  may  be  said 
concerning  physical  transformations  as  well.  If  a  definite 
mass  of  a  gas  is  selected  under  a  specific  temperature  and 
pressure,  it  will  occupy  a  definite  volume.  If,  however,  this 
definite  mass  be  subjected  to  different  pressures  and  tem- 
peratures, the  volume  which  it  occupies  may  vary  greatly, 
and  hence  the  volume  which  this  constant  mass  occupies 
depends  upon  the  pressure  and  temperature ;  that  is,  the 
values  for  the  pressure,  p,  the  temperature,  /,  and  the  volume, 
V,  are  so  related  to  one  another  that  simultaneous  values  of 
any  two  determine  the  functional  relation.  This  may  be 
expressed  mathematically,  V  =  f  (p,t).  This  equation  is 
known  as  the  Equation  of  State.  In  the  functional  relation 
the  volume  which  a  given  mass  occupies  depends  upon  the 
temperature  and  pressure.  The  pressure,  p,  and  the  tem- 
perature, /,  are  spoken  of  as  the  independent  variables,  and 
the  volume,  V,  as  the  dependent  variable,  because  its  value 
depends  upon  the  values  arbitrarily  selected  for  p  and  /. 
By  keeping  one  of  these  independent  variables  constant  it  is 
possible  to  determine  what  relation  exists  between  the  de- 
pendent variable  and  the  other  independent  variable. 

i.   Assume  a  constant  mass  of  gas. 

The  volume  which  it  occupies  depends  upon  p  and  /. 
Then  F  is  a  dependent  variable. 

If  we  assume  t  and  the  mass  constant,  V  depends  on  p, 

18 


THE  GAS  LAW  19 

Let  volume  at  pressure  p  be  V  and  the  volume  at  pressure  pi 
beVi. 

Now  by  experiment  we  find  that  if  1000  cc.  of  gas  is  at 
500' mm.  pressure,  then  the  volume  will  be  500  cc.  if  the  pres- 
sure is  increased  to  1000  mm.  That  is, 

1000  cc. :  500  cc. :  :  1000  mm. :  500  mm. 

or 
V:Vn  :pnp. 

If  the  temperature  is  constant,  the  volumes  are  inversely 
proportional  to  the  pressures.  This  is  Boyle's  Law. 

2.  Now  assume  pressure  and  mass  constant  and  vary  the 
temperature.  Gay  Lussac  found  experimentally  that  if  100 
cc.  of  gas  at  o°  C.  were  heated,  the  volume  was  136.65  cc.  at 
100°  C.  or  an  increase  of  36.65  cc.  for  a  change  of  100°  C.,  or 
0.3665  cc.  for  i°.  The  change  for  i  cc.  is  y^  of  this,  or 
0.003665  cc.  That  is,  for  every  increase  of  one  degree  cen- 
tigrade the  volume  is  increased  this  proportional  amount, 
or  i  cc.  increases  0.003665  cc.  per  degree  C.  But  0.003665  = 
1/273.  Any  volume  of  gas  at  o°  C.  will  increase  for  any 

number  of  degrees  of  change  of  temperature  times  the 

273 
original  volume. 

Let  Fo  =  volume  of  mass  of  gas  at  /0,  at  pressure  po. 

V   =  volume  of  mass  of  gas  at  t,  and  at  the  same 

pressure. 

Then  V  —  Vo  =  increase  in  volume 
and  t  —  to  =  change  in  temperature. 

But  a  gas  increases  1/273  of  the  original  volume  per  de- 
gree; then  1/273  times  Vo  =  increase  in  volume  per  degree. 

t  —  toX  — -  =  increase  for  change  of  temperature  t  —  to  on 

273 
the  centigrade  scale. 

But  the  increase  in  volume  is  V  —  Vo, 

hence  V  -  V,  =  ^— ^  X  F0  which  becomes  V  ~  Vo  =  ^-°- 
273  ^o  273 


20  ,  PHYSICAL   CHEMISTRY 

We  are  expressing  our  temperature  as  temperature  differ- 
ences on  the  arbitrarily  selected  centigrade  scale. 

The  equation  -  -  =  -  -  could  be  simplified  mathe- 
^o  273 

matically  if  we  were  to  take  /0  =  273  and  substitute  in  the 
above  equation.  The  zero  of  the  centigrade  scale  then  would 
become  273  centigrade  divisions  above  the  zero  point  on  our 
new  temperature  scale.  This  new  point  is  known  as  the 
Absolute  Zero  and  is  found  to  be  practically  the  same  as  the 
Absolute  Zero  on  the  thermodynamic  scale.  The  readings 
on  the  centigrade  scale  equal  273  -f-  t  on  the  Absolute 
scale,  or  T  =  TQ  +  t.  Now  having  assigned  these  values, 

the  equation  becomes  —  --  -,  from  which  we  ob- 

Vo  -To 

tain  —  =  —  or  V  :  Vo  :  :  T  :  To  which  states  that  the  volumes 

Vo        TQ 

of  a  given  mass  of  gas  under  constant  pressure  are  directly 
proportional  to  the  Absolute  temperatures.  This  is  Charles' 
or  Gay  Lussac's  Law. 

These  two  laws  can  be  combined  into  one  expression  by 
assuming  a  constant  mass  of  the  gas  :  and  then  (i)  with  the 
temperature  constant,  change  the  pressure  ;  and  then  (2)  with 
the  pressure  constant,  change  the  temperature. 

Assuming  the  mass  constant  and  the  temperature  constant, 
then  let  V0  =  the  volume  of  the  gas  at  pressure  po  and  tem- 
perature TQ. 

Vi  =  the  volume  of  the  gas  at  pressure  pi  and  tem- 
perature TV 

Then  according  to  Boyle's  Law 

Vo  :  Vi  :  :  pi  :  po. 
Solving  for  Vi,  we  have 


pi 


THE  GAS  LAW  21 

Now  change  the  temperature  on  this  new  volume  keep- 
ing the  pressure  constant,  pi  =  p%;  we  have  according  to 
Charles'  or  Gay  Lussac  's  Law  : 

Vi  :  V2  :  :  Ti  :  T2  or  ViT2  =  V2Ti. 


Substituting  the  value  of  Vi  =        -°  we  have        **  =  y2Ti. 

pi  pi 

Now  eliminate  intermediate  values  and  remember  To  = 

~\7  >>  T* 

i  and  pi  =  p2.     We  have     °^°   2  =  V2T0.     Rearranging,  we 


have 

-To          -/2 

which  is  an  expression  for  the  combined  laws  of  Gay  Lussac 
and  Boyle. 

Now  it  is  possible  to  change  these  last  values  to  new  ones 

and  obtain  similarly  the  same  relation.     —  ^  =  —  ^,  or  in 

Tz         13 

general  the  initial  volume  multiplied  by  its  corresponding 
pressure  divided  by  its  corresponding  temperature,  is  equal 
to  any  other  volume  times  its  corresponding  pressure  divided 

by  its  corresponding  temperature.     -4p  =  —  *,  which  is  con- 

To         / 

stant, 

or  X    =  constant  :  Vp  =  KT.  (A) 


ANOTHER  DEVELOPMENT  OF  THE  GAS  LAW  EQUATION 

It  has  been  shown  experimentally  that  if  we  take  a  definite  mass  of 
gas,  the  volume  it  occupies  will  be  dependent  on  its  temperature  and 
pressure.  That  is,  keeping  the  mass  constant, 

V  =  f(p,  t]  or  it  may  be  stated  that 
p  =  f(V,  t)  and  also,  /  =  f(V,  p). 

Gay  Lussac  showed  by  experiment  that  when  the  volume  is  constant, 
the  change  in  pressure  is  directly  proportional  to  the  change  in  tern- 


22  PHYSICAL   CHEMISTRY 

perature.  Assuming  this  to  be  true  for  the  entire  range  of  temperature 
and  pressure  the  functional  relation  p  =  f(V,  t)  is  expressed  by  the 
equation 

p  -  po  =  k(t  -  t0)  (i) 

where  k  may  be  a  function  of  the  volume. 
It  will  be  recalled  that 

y  =  ax  +  b 

is  the  ordinary  equation  of  a  straight  line,  in  which  a  represents  the 
tangent  of  the  angle  which  the  line  makes  with  the  x  axie  and  b  repre- 
sents the  intercept  on  the  y  axis.     Any  given  point  (xf,  y')  on  this  line 
must  satisfy  the  equation  which  gives  y'  =  ax'  +  b. 
Eliminating  b  we  get 

y  -  y'  =  a(x  -  x').  (2) 

This  is  the  equation  of  a  straight  line  through  the  point  (#',  y')  making 
an  angle,  whose  tangent  is  a,  with  the  x  axis. 

Equation  (i)  is  the  same  form  as  equation  (2).  Therefore  the  equa- 
tion 

p-po  =  k(t  -to) 

represents  a  straight  line  through  a  given  point  (to,  po)  making  an  angle 
with  the  temperature  axis  whose  tangent  is  k. 

Since  we  may  arbitrarily  select  (/0,  po),  let  us  assume  it  to  be  the 
melting  point  of  ice  under  atmospheric  pressure.  This  is  the  zero 
on  the  ordinary  centigrade  scale.  That  is,  t  =  o  and  p  =  the  pressure 
of  one  atmosphere.  Substituting  to  =  o  in  equation  (i)  we  get 

P  -  po  =  kt.  (3) 

In  Fig.  i  let  the  melting  point  of  ice  (to,  po),  on  the  pressure  axis 
and  some  distance  above  the  temperature  axis,  be  represented  by  A. 

Now  we  know  by  experiment  that,  when 
;>t      the  temperature  is  raised,  the  pressure 
is  increased.     Therefore,  any  other  point 
representing  a  greater  pressure  will  be  to 
the  right   and   above  the   point   A,  as 
point  B  (pi,ti).     Then  the  straight  line 
— —      AB  through  these  two  points  will  be  the 
FIG.  i.  locus  of  equation  (3). 

The  value  of  po  is  taken  as  one  atmos- 
phere above  absolute  zero  pressure,  as  we  selected  the  melting  point  at 
the  pressure  of  one  atmosphere,  but  the  value  of  to  was  assumed 


THE   GAS  LAW  23 

without  reference  to  any  absolute  zero  of  temperature.  Therefore, 
where  the  locus  cuts  the  temperature  axis  is  represented  the  absolute 
zero  of  pressure,  and  it  is  of  some  advantage  to  us,  to  take  the  origin 
of  the  coordinants  at  this  point  0.  If  we  do  this,  all  values  of  pres- 
sures remain  the  same,  but  the  value  of  each  temperature  will  be 
increased  by  the  distance  between  this  point  O  and  the  point  A',  the 
origin  of  our  old  system  of  axes,  i.e.  the  distance  OA ',  which  we  will 
designate  TV  So  if  we  refer  the  temperatures  to  our  new  coordinate 
axis  by  T,  then 

T  =  To  +  t  or  /  =  T  -  T0. 

Substituting  this  value  in  equation  (3)  we  get 

p-pQ  =  k(T-  To).  (4) 

Equation  (4)  may  be  written 

p  -  kT  =  Po  -  kT0.  (4') 

Since  the  locus  of  this  equation  passes  through  the  origin,  the  coordinates 
(0,  O)  of  the  origin  must  satisfy  it. 
Substituting,  we  have 

o  —  ko  =  po  —  kTQ  or  po  —  kT0  =  o. 

Substituting  this  value  back  in  equation  (4')  it  then  becomes  p  —  kT 
=  o  or 

P  =  kT.  (5) 

This  is  a  simple  form  of  the  equation  (4)  representing  the  same  locus. 

Now,  equation  (4)  was  developed  directly  from  Gay  Lussac's  gener- 
alization, which,  as  he  showed  experimentally,  is  true  for  any  gas  assum- 
ing the  mass  and  volume  constant.  Therefore,  equation  (5)  is  true 
for  any  gas. 

Solving  this  equation  for  k,  we  have 

*-f  (50 

Now  Boyle's  generalization  is,  that  keeping  the  mass  and  tempera- 
ture constant,  the  pressures  are  inversely  proportional  to  the  volume ; 
or  as  we  saw,  V:  V\\:p\:p  which  becomes  Vp  =  V\pit  or  keeping  the 

mass  and  temperature  constant  the  product  of  the  volume  and  pressure 

ip 

is  a  constant,  i.e.  pV  =  K\,  or  p  =  —±,  the  pressure  is  inversely  pro- 
portional to  the  volume. 


'  '  .  *' 

24  PHYSICAL   CHEMISTRY 


y 
Applying  this  generalization  to  (5')  we  have  k  =-y»  and  remembering 

T£ 

that  T  is  constant  we  then  have  k  =  — -.     This  means  that  k  is  con- 
stant only  when  the  mass  and  volume  are  constant ;  but  that  when  the 

volume  is  increased,  k  is  decreased. 

jp 
Substituting  this  value  of  k  in  equation  (5),  we  have  p  =  —  T  or 

pV  =  KiT.  (6) 


DISCUSSION    OF   THE    CONSTANT    OF    THE    GAS    LAW 

Equation  (A)  is  developed  from  Boyle's  and  Gay  Lussac's 
generalization,  assuming  a  constant  mass.  This  is  true, 
however,  only  in  the  case  of  a  true  gas,  which  is  a  hypo- 
thetically  perfect  gas,  wherein  the  internal  energy  is  de- 
pendent on  the  temperature  only.  Oxygen,  hydrogen,  air, 
and  nitrogen  so  nearly  conform  to  perfect  gases  that  for 
practical  purposes  they  may  be  considered  as  ideally  perfect 
and  obeying  the  laws  of  perfect  gases. 

The  equation  K  =  ^  (i) 

means  that  if  the  volume  of  a  given  mass  of  gas  is  changed, 
the  pressure  or  the  temperature,  or  both  temperature  and 
pressure,  must  change  so  that  the  pressure  multiplied  by  the 
volume  divided  by  the  absolute  temperature  shall  always  be 
the  same. 

By  experiment  we  find  that  keeping  the  pressure  and 
temperature  constant,  the  volumes  of  different  masses  of  the 
same  gas  are  directly  proportional  to  the  masses,  i.e. 
V:  Vi:  :M:  Mi,  where  V  is  the  volume  of  mass  M,  and  V\ 
is  the  volume  of  mass  Mi.  So,  different  masses  of  the  same 
gas  have  different  values  of  K.  Also,  by  experiment,  we 
know  that  equal  masses  of  different  gases  have  different 
volumes  under  the  same  conditions  of  temperature  and 


THE  GAS  LAW  25 

pressure.     In  general,  then,  we  must  use  different  values  of 
K  for  equal  masses  of  the  different  gases. 

The  value  of  K  for  unit  mass  of  a  given  gas  is  denoted 
by  r.  Let  us  denote  the  volume  of  unit  mass  of  a  gas  by  v, 
then  equation  (i)  becomes 

pv  =  rT.  (2) 

Since  r  has  different  values  for  different  gases,  the  gas 
must  be  specified  when  using  equation  (2),  and  r  is  called 
the  specific  gas  constant. 

It  follows,  then,  that  K  for  any  mass  M  is  equal  to  Mr  or 
K  =  Mr.  (3) 

If  we  choose  the  masses  of  the  different  gases  so  as  to  give 
the  same  volumes  at  the  same  temperature  and  pressure,  K 
has  the  same  value  for  every  gas,  according  to  equation  (i). 
By  experiment  we  find  that  the  molecular  weight  of  every 
chemical  compound  in  the  gaseous  state  occupies  the  same 
volume  at  a  definite  pressure  and  temperature. 

If  the  molecular  weight  of  a  gas  is  chosen,  the  value  of 
K  is  denoted  by  R.  If  m  is  the  molecular  weight,  then 
from  equation  (3) 

R  =  mr  (4) 

and  equation  (i)  becomes 

PV  =  RT.  (5) 

Since  the  value  of  R  is  the  same  for  all  gases,  R  is  called 
the  Universal  Gas  Constant. 

The  molecular  weight  of  a  compound  in  grams  is  called 
the   gram-molecular  weight,   or  mole.     If   any  number   of 
moles,  n,  are  used,  the  more  general  form  of  the  equation  is 
pV  =  nRT.  (6) 

Since  n  =  •£-,'  where  g  is  the  weight  in  grams,  we  may  sub- 
stitute in  equation  (6)  and  obtain 

(7) 


26  PHYSICAL  CHEMISTRY 

Solving  equation  (5)  pV  =  RT  for  R,  we  have  R  —  £-?-• 
But  we  saw  that  for  the  same  mass  of  gas  under  different 


conditions  of  pressure  and  temperature  we  have  Ki  = 

/  T          To 

therefore, 


And  by  definition  we  have  p0  =  the  pressure  of  one  atmos- 
phere, which  is  equivalent  to  760  mm.  of  mercury,  i.e.  to 
the  pressure  of  a  column  of  mercury  of  one  sq.  cm.  cross- 
section  and  76  cm.  high,  or  to  the  weight  of  76  cubic  centi- 
meters of  mercury.  Now,  since  one  cubic  centimeter  of 
mercury  weighs  13.6  grams,  76  cc.  will  weigh  76  X  13.6,  or 
1033-6  grams.  The  pressure  of  one  atmosphere  is  therefore 
equivalent  to  1033.6  grams  per  unit  area  of  one  square  cen- 
timeter. The  temperature  To  =  273°  absolute  on  the  cen- 
tigrade scale,  while  Vo  is  denned  as  the  volume  of  one 
gram-molecule  of  oxygen,  O2,  i.e.  32  grams  of  oxygen. 
Since  the  weight  of  one  liter  of  oxygen  is  1.429  grams,  this 

volume  of  oxygen  will  be     32    ,  or  22.4  liters.     Therefore, 

1.429 

Vo  =  22.4  liters,   which   is  designated    the   gram-molecular 
volume. 

Substituting  these  values  in  our  equation  R  =  ^-=-* ,  we 

To 

have       R  =  *       22'4  =  0.08204  liter-atmosphere  per  degree, 

273 
of  R=s  1033-6  X  22400  =  84?78o    gram.centimeters    per 

2  73  degree. 

It  is  customary  in  Thermodynamics  to  express  the  terms 
in  the  Gas  Law  Equation  in  the  English  system  and  the 
Fahrenheit  temperature  scale. 

If  we  have  a  mass  of  gas  at  the  temperature  of  melting 
ice,  32°  F.,  and  at  atmospheric  pressure,  then 


THE  GAS  LAW  27 

PQ  =  i    atmosphere  =  14.6967    Ib.    per   square    inch  = 
2116.32  Ib.  per  square  foot. 
To  =  491.6°  absolute  on  the  Fahrenheit  scale. 
v  =  volume  of  unit  weight  of  the  gas  (i  pound). 
B  =  characteristic  gas  constant  and  is  the  symbol  used  in 
place  of  r  when  the  English  system  of  units  is  employed. 

Then  equation  (2)  becomes 

pv  =  BT.  (B) 

From  equation  (4)  we  obtain  R  =  mB.     If  p  is  the  mass 

of  unit  volume  of  the  gas,  we  have  v  =  —  • 

P 

Substituting  for  v  and  B  their  values  in  equation  (B),  we 
obtain 

£  =  RT 

P      m 
Solving  for  R,  we  get 

R  =  *%•  (C) 

pT 

If  m  and  p  are  known  for  any  gas,  R  can  be  calculated. 

For  oxygen  p  =  0.089222  Ib.  per  cubic  foot  at  atmos- 
pheric pressure  and  32°  F.  and  m  =  32. 

Substituting  in  above  equation,  we  have 


R  =    »'v    '«  =  I544  ft--lb-  per  degree- 

0.089222  X  491.6 

The  universal  gas  constant  R  is  then  equal  to  1544  ft.-lb. 
per  degree. 

From  this  value  of  R,  the  characteristic  or  specific  con- 
stant B  of  any  gas  may  be  determined  if  its  molecular  weight 
is  known. 

For  carbon  dioxide  we  have  B  =  I^44  =  35.09. 

44 

It  is  often  convenient  to  express  the  density  and  the 
volume  of  unit  weight  of  a  gas  in  terms  of  the  molecular 


28  PHYSICAL  CHEMISTRY 

weight  m  when  referred  to  standard  conditions  of  tempera- 
ture and  pressure. 


From  R  =  ~,  we  have  p  =        ,   hence   substituting  the 
pi  Rl 

numerical  values 

p  =  2116.3  lb.  Per  sq.ft.,  R  =  i544ft.-lb.  per  degree,  and 
T  =  491.6°  F.,  we  have 

=   2116.3  Xm  =0-002788  m  rb.  per  cubic  foot  per 

1544  X  491-6 
degree. 

And  for  the  normal  specific  volume  we  have 

X  4T-6  =  ^^5  cubic  feet  per  pound. 


p      pm  2116.3  m  m 


CHAPTER   IV 
DETERMINATION  OF  MOLECULAR  AND  SYMBOL  WEIGHTS 

THE  method  employed  for  the  determination  of  symbol 
weights  at  present  is  virtually  that  of  Cannizzaro,  wherein 
the  weight  of  the  gram-molecular  volume  is  obtained  for  a 
large  number  of  gaseous  compounds  containing  that  element, 
and  the  greatest  common  divisor  of  these  quantities  of  the  - 
element  occurring  in  the  gram-molecular  volume  is  selected 
as  the  symbol  weight  of  the  element  and  is  also  termed  the 
atomic  weight. 

We  selected  arbitrarily  as  the  unit  volume  of  combina- 
tion the  volume  occupied  by  one  gram-molecule  of  oxygen, 
i.e.  32  grams  of  oxygen  under  the  standard  conditions  of 
temperature  and  pressure.  For  the  standard  conditions  we 
have  defined  the  standard  pressure  as  the  pressure  of  one 
atmosphere  at  sea-level  and  latitude  45°,  or  760  mm.  of 
mercury,  and  the  temperature  as  the  zero  on  the  Centigrade 
scale  or  273°  absolute.  The  unit  for  volume  measurements 
is  the  cubic  centimeter,  one  thousand  of  which  are  designated 
a  liter.  The  weight  of  one  cubic  centimeter  of  oxygen 
under  standard  conditions  of  temperature  and  pressure  has 
been  determined  very  accurately  and  is  found  to  be  0.001429 
gram.  One  liter  weighs  1.429  grams.  The  volume  oc- 
cupied by  one  gram  molecule  of  oxygen,  i.e.  32  grams,  is 
32  -r-  1.429  =  22.4  liters  under  the  standard  conditions  of 
temperature  and  pressure.  Hence,  we  designate  22.4  liters 
as  the  gram-molecular  volume,  as  it  is  the  volume  of  one  gram 
molecule,  i.e.  the  volume  which  the  molecular  weight  of  a 

29 


30  PHYSICAL  CHEMISTRY 

gas  expressed  in  grams  would  occupy  under  standard  con- 
ditions. 

Density  Relations.  —  We  have  seen  that  pV  =  nR  T  holds 
generally  for  gases.  Let  us  assume  that  it  does  for  those 
with  which  we  are  dealing,  and  let  g,  —  grams  of  a  gaseous 
body  we  select  as  our  standard,  g  =  grams  of  some  other 
gas  measured  at  the  same  pressure  and  temperature,  and 
occupying  the  same  volume  as  the  standard,  ma  the  weight 
of  a  gram-molecular  volume,  22.4  liters  of  the  standard,  m 
the  weight  of  a  gram-molecular  volume,  22.4  liters  of  the 
other  gas.  From  the  definition  of  the  number  of  formula 

weights  of  any  gas  we  have  na  =  —  for  the  standard,  and 

nig 

n  =  -&-  f  or  the  other  gas.     Substituting,  the  Gas  Law  Equa- 
tion becomes 

d) 


and  pV  =      RT.  (2) 

Solving, 


. 
RT     ma         RT     m         ma     m 

g  t  g 

Solving  this  for  m,  we  have  m  =  —  m,.     But  since  5  =  —  > 

6*  &« 

we  have  m  =  smt. 

Since  air  obeys  the  Generalized  Gas  Law  very  closely,  it 
is  considered  for  this  reason  a  very  good  standard.  The 
weight  of  air  has  been  determined  very  accurately,  and  it 
has  been  found  that  one  liter  of  air  at  o°  C.  and  760  mm. 
pressure  at  sea-level  in  the  latitude  of  45°  weighs  1.293 
grams.  If  one  liter  under  standard  conditions  weighs  1.293 
grams,  then  22.4  liters,  the  gram-molecular  volume,  weighs 
28.96  grams.  If  we  now  substitute  this  value  for  m,  in  the 
equation  above,  we  have  m  =  s  X  28.96.  That  is,  the 
molecular  weight  of  a  gas  is  equal  to  its  specific  gravity 


DETERMINATION  OF  MOLECULAR  WEIGHT  31 

expressed  in  terms  of  air  multiplied  by  28.96,  which  is  the 
weight  of  22.4  liters  of  our  standard  (air).  So,  to  determine 
the  molecular  weight  of  a  gaseous  substance  we  need  only 
determine  its  specific  gravity  with  respect  to  air,  and  mul- 
tiply this  by  28.96.  This  is  nothing  more  than  finding  the 
weight  of  the  gas  that  would  occupy  one  gram-molecular 
volume  under  standard  conditions. 

It  is  not  even  necessary  to  determine  the  specific  gravity 
with  respect  to  air,  but  any  other  gas  may  be  used  as  a 
standard.  In  that  case,  however,  we  have  to  multiply  the 
specific  gravity  with  reference  to  that  particular  gas  as  a 
standard,  by  an  entirely  different  factor.  For  instance,  if 
we  use  hydrogen  as  our  standard,  the  weight  of  the  gram- 
molecular  volume,  22.4  liters  of  hydrogen,  is  2.016  grams, 
and  the  equation  would  then  become  m  =  SH  X  2.016.  If  we 
use  oxygen  as  the  standard,  we  have  m  =  s0  X  32,  i.e.  the 
specific  gravity  of  the  gas  with  reference  to  oxygen  multi- 
plied by  32  is  equal  to  the  molecular  weight  of  the  gas. 

From  what  has  preceded,  in  order  to  determine  the  molecu- 
lar weight  of  a  gaseous  body,  all  we  need  to  do  is  to  deter- 
mine the  specific  gravity,  and  from  this  to  calculate  the 
amount  by  weight  that  will  occupy  the  gram-molecular 
volume,  22.4  liters,  under  the  standard  conditions  of  tem- 
perature and  pressure.  This  number  we  call  the  formula 
weight,  or  molecular  weight. 

The  two  chief  methods  for  the  determination  of  vapor 
densities  are  the  Dumas  method  and  the  Victor  Meyer 
method.  Only  a  brief  description  of  the  principles  of  these 
methods  will  be  given.  The  technique  of  the  operations 
may  be  found  in  the  laboratory  manuals  on  physico-chemical 
methods. 

Dumas'  Method.  —  A  weighed  glass  bulb  of  about  200 
cc.  capacity,  into  which  some  of  the  substance  has  been  in- 
troduced, is  immersed  in  a  water-bath,  the  temperature  of 
which  is  kept  about  30°  above  the  boiling-point  of  the  sub- 


32  PHYSICAL   CHEMISTRY 

stance.  When  the  substance  is  all  in  the  form  of  vapor, 
the  end  of  the  bulb  is  sealed,  at  which  time  the  temperature 
of  the  bath  is  recorded,  and  also  the  barometric  pressure. 
The  bulb  is  then  removed,  cooled,  and  weighed,  and  the 
weight  of  substance  found.  By  filling  with  water  at  known 
temperature  and  weighing,  the  weight  of  the  water  is  found  by 
difference.  The  volume  which  this  weight  occupies  is  found 
from  tables  of  densities  of  water  at  different  temperatures. 
Then,  knowing  the  volume,  temperature,  and  weight  of  the 
substance,  and  the  barometric  reading,  the  density  and 
specific  gravity  can  readily  be  calculated.  This  method  is 
but  little  used  at  present. 

The  Victor  Meyer  Method.  —  The  Victor  Meyer  method 
consists  in  measuring  the  increase  in  volume  of  a  quantity 
of  air,  caused  by  introducing  into  it  a  weighed  quantity  of 
the  substance  whose  density  is  to  be  determined,  and  vaporiz- 
ing it.  The  vaporized  substance  displaces  an  equal  volume 
of  air,  and  this  displaced  volume  of  air  is  collected  and 
measured,  and  at  the  same  time  its  temperature  and  the 
barometric  pressure  are  observed  and  recorded.  This 
then  gives  the  weight  of  the  substance  taken,  and  the 
volume,  temperature,  and  pressure,  from  which  the  density, 
specific  gravity,  and  the  molecular  weight  can  readily  be 
calculated. 

Molecular  Formulae  and  Formula  Weight.  —  Having  just 
seen  how  the  molecular  weight  of  a  gaseous  substance  can  be 
obtained,  we  can  ascertain  the  formula  which  expresses  not 
only  the  relative  quantities  of  the  component  elements,  but 
also  the  weight  of  the  substance  which  occupies  a  gram- 
molecular  volume.  Such  formulae  we  designate  as  molecu- 
lar formulae,  and  they  are  now  employed  to  represent  the 
quantity  of  the  substance  designated  by  the  molecular 
weight,  whether  it  exists  in  the  gaseous,  liquid,  or  solid 
condition.  Suppose  benzene  is  found  by  analysis  to  con- 
tain 92.25  per  cent  of  carbon  and  7.75  per  cent  of  hydrogen. 


DETERMINATION  OF  MOLECULAR  WEIGHT  33 

Then  in  every  100  g.  of  the  substance  we  should  have  as 

Q  2    2  C 

many  symbol  weights  of  carbon  as  -      — ,  or  7.69,  and  of 

hydrogen  as -^~r,    or    7.69.     That    is,    for    every    symbol 

weight  of  carbon  there  is  one  of  hydrogen ;  there  are  the 
same  number  of  symbol  weights  of  the  two  elements.  As- 
suming the  simplest  number  present,  the  empirical  formula 
is  CH.  The  specific  gravity  of  benzene  with  respect  to 
oxygen  is  2.47  at  100°  C.  The  molecular  weight  is,  there- 
fore, 2.47  X  32  =  79.04,  which  is  nearly  six  times  the  sum 
of  the  symbol  weights  of  carbon  and  hydrogen  as  repre- 
sented by  the  empirical  formula.  The  molecular  formula  is 
therefore  CeHe,  and  the  molecular  weight  is  78.06. 

Symbol  Weight.  —  The  symbol  (or  atomic)  weight  of  an 
element  may  be  deduced  from  the  molecular  weights  of  its 
gaseous  elements  in  the  following  manner  :  In  order  to  ascer- 
tain the  symbol  weight  of  hydrogen  a  large  number  of  gaseous 
compounds  are  selected  which  contain  hydrogen,  and  the 
molecular  weight  of  these  substances  is  ascertained  from 
density  and  specific  gravity  determinations.  In  Table  I  are 
given  the  names  of  the  substances,  in  the  second  column  the 
molecular  weights,  i.e.  the  grams  of  the  substance  that  occupy 
22.4  liters  under  standard  conditions  of  temperature  and 
pressure,  while  in  the  third  column  is  given  the  number  of 
grams  of  hydrogen  found  by  analysis  in  the  amount  of  the 
substance  represented  by  the  molecular  weight  given  in  the 
second  column.  In  the  last  column  is  the  greatest  common 
divisor  of  the  weights  of  hydrogen  in  column  three,  times 
the  factor  by  which  it  is  multiplied  to  give  the  amount  of 
hydrogen  in  these  various  gram-molecules  of  the  gases. 
Now  in  the  case  of  hydrogen,  the  greatest  common  divisor 
of  the  quantities  of  this  element  appearing  in  the  gram- 
molecules  of  these  various  substances  is  i  g. ;  hence  we  take 
the  symbol  weight  of  hydrogen  to  be  i.  Proceeding  in  a 


34 


PHYSICAL   CHEMISTRY 


similar  manner,  we  can  compile  tables  for  other  elements 
such  as  given  for  nitrogen. 

TABLE  I 


HYDROGEN 

NITROGEN 

Compound 

1 

2 

3 

Compound 

1 

2 

3 

Hydrochloric  acid  .     .     . 

S6.S 

i 

Ammonia          .     . 

17 

14 

Xi4 

Hydrobromic  acid        .     . 

81 

i 

Nitric  oxide      .    . 

30 

14 

Xi4 

Hydriodic  acid    

128 

i 

Nitrogen  peroxide 

46 

14 

Xi4 

Water  

18 

2 

X 

Methyl  nitrate 

77 

14 

Xi4 

Hydrogen  sulphide      .     . 

34 

2 

X 

Cyanogen  chloride 

61.5 

14 

Xi4 

Hydrogen       

2 

2 

X 

Nitrogen      .     .     . 

28 

28 

Xi4 

Ammonia       

17 

3 

3  X 

Nitrous  oxide  .     . 

44 

28 

Xi4 

Hydrogen  phosphide   .     . 

34 

3 

3X 

Cyanogen  .      .     . 

52 

28 

Xi4 

Methane    

16 

4  X 

_,    _  __ 

Ethane      

30 

6 

6X 

(j.  C.  D.  —  14 

G.  C.  D.  =  i 

In  general,  if  an  element  has  a  large  number  of  volatile 
compounds  whose  molecular  weights  can  be  obtained  from 
their  vapor  densities,  the  symbol  weight  may  be  obtained 
in  the  manner  just  illustrated.  As  the  weights  of  the  ele- 
ment that  are  contained  in  the  molecular  weights  of  its  com- 
pounds must  be  equal  to  its  symbol  weight  (atomic  weight) 1 
or  must  be  multiples  of  it,  if  we  take  the  greatest  common 
divisor  of  these  weights,  it  must  be  a  simple  multiple  of  the 
symbol  weight,  or  the  symbol  weight  itself.  It  is  hardly 
probable,  however,  that  where  there  are  a  large  number  of 
volatile  compounds  of  the  element,  the  common  divisor  is  a 
multiple  of  the  symbol  weight,  but  it  is  possible  that  another 
substance  may  be  discovered,  the  molecular  weight  of  which 
contains  a  weight  of  the  given  element  which  is  not  a  mul- 
tiple of  our  greatest  common  divisor.  Thus  the  symbol 
weight  as  determined  in  the  manner  indicated  above  would 

1  The  term  symbol  weight  has  been  used  in  this  book  for  what  is 
usually  termed  atomic  weight.  Atomic  weight  is  discussed  in  the  fol- 
lowing chapter. 


DETERMINATION  OF  MOLECULAR  WEIGHT  35 

not  be  the  true  one ;  however,  those  so  obtained  have  a 
high  degree  of  probability. 

If,  however,  there  are  but  very  few  volatile  compounds 
containing  the  element,  which  are  available  for  vapor  den- 
sity determinations,  the  method  may  fail.  There  are  a 
number  of  other  methods,  however,  for  obtaining  the 
molecular  weight  of  substances,  and  these  values  may  be 
used  in  our  tabulations  just  as  well  as  those  obtained 
through  the  vapor  density  relations. 

Some  of  the  more  recently  discovered  elements,  the  gases 
argon,  helium,  xenon,  etc.,  are  supposed  to  be  elementary, 
and  to  contain  only  one  symbol  weight  in  their  gram-molec- 
ular weight.  As  they  form  no  compounds,  we  cannot  use 
the  method  just  suggested  for  determining  the  symbol 
weights.  If,  however,  we  remember  that  the  molecular 
weight  is  the  weight  of  the  substance  that  occupies  22.4  1. 
under  standard  conditions  of  temperature  and  pressure,  we 
can  find  the  molecular  weight  by  ascertaining  the  number  of 
grams  of  the  gas  that  are  contained  in  a  gram-molecular 
volume. 

We  have  just  seen  that  by  our  volumetric  method  we  may 
determine  which  of  several  quantities  is  the  correct  one  for 
the  symbol  weight  of  an  element ;  but  in  order  to  determine 
these  values  with  a  high  degree  of  accuracy,  it  is  necessary 
to  employ  quantitative  gravimetric  methods.  By  the  above 
methods  it  is  possible  to  determine  which  of  a  number  of 
values  is  the  correct  one  for  both  the  symbol  weight  of 
elements  and  also  the  molecular  weight  of  the  compounds. 

The  International  Committee  on  Atomic  Weights  publishes 
periodically  a  table  of  values,  which  it  designates  the  Atomic 
Weights,  based  upon  the  unit  of  oxygen  taken  as  16  and 
representing  relative  weights. 


CHAPTER  V 
ATOMIC  AND   MOLECULAR  THEORIES 

FROM  observed  experimental  scientific  facts,  conjectures 
are  made  as  to  how  other  substances  react  and  these  are 
employed  as  the  starting  point  for  additional  experimentation 
and  investigation.  This  is  regarded  as  a  working  hypothesis. 
While  a  hypothesis  is  a  tentative  speculative  conjecture  of 
the  causes  for  the  observed  facts,  it  is  an  assumption 
which  goes  beyond  these  observed  facts  and  is  to  be  used  as 
a  basis  for  their  arrangement  and  classification  as  well  as 
that  of  all  other  facts  of  the  same  class. 

When  a  hypothesis  explains  all  of  the  known  facts,  then 
it  ranks  as  a  theory.  A  theory  is  defined  as  "  a  systematic 
generalization  seriously  entertained  as  exclusively  or  emi- 
nently accounting  for  a  series  or  group  of  phenomena."  As 
soon  as  a  number  of  facts  are  collected  which  the  theory 
does  not  accord  with  or  explain,  the  theory  becomes  unten- 
able, and  a  new  one  has  to  be  formulated  which  will  har- 
monize with  the  known  facts.  We  have  hypotheses  and 
some  theories  undergoing  frequent  changes,  as  they  always 
contain  unproved  assumptions. 

How  our  path  of  progress  is  blazed  out  and  marked  is 
indicated  by  the  following  quotations  from  two  noted  pioneer 
investigators. 

Tyndall  states :  "  We  are  gifted  with  the  power  of  im- 
agination, and  by  this  power  we  can  enlighten  the  darkness 
which  surrounds  the  world  of  the  senses.  Bounded  and  con- 
ditioned by  cooperant  reason,  imagination  becomes  the 

36 


ATOMIC  AND   MOLECULAR  THEORIES  37 

mightiest  instrument  of  the  physical  discoverer.  ...  By 
his  observations  and  reflections  in  the  domain  of  fact  the 
scientific  philosopher  is  led  irresistibly  into  the  domain  of 
theory,  his  final  repose  depending  on  the  establishment  of 
absolute  harmony  between  both  domains." 

Faraday  wrote :  "  The  world  little  knows  how  many  of 
the  thoughts  and  theories  which  have  passed  through  the 
mind  of  an  investigator  have  been  crushed  in  silence  and 
secrecy  by  his  own  severe  criticism  and  adverse  examina- 
tion ;  that  is,  in  the  most  successful  instances  not  a  tenth  of 
the  suggestions,  the  hopes,  the  wishes,  and  the  preliminary 
conclusions  are  realized." 

THE  ATOMIC  THEORY 

That  matter  is  not  continuous,  but  composed  of  minute, 
indivisible  particles  or  atoms  is  a  very  ancient  idea.  This 
idea  was  purely  speculative  and  not  founded  on  observation 
or  experiment.  Democritus  (460  B.C.)  attributed  the  dif- 
ference in  substances  to  the  atoms  of  which  they  are  con- 
stituted, and  these  atoms  he  considered  to  be  different  in 
size,  shape,  position,  and  motion.  Lucretius  (50  A.D.)  for- 
mulated the  ideas  of  the  atomic  constitution  of  matter  in 
practically  the  form  in  which  it  is  familiarly  expressed  to-day. 
The  following  are  his  conclusions  : 

1 .  In  a  solid  the  atoms  are  squeezed  closely  together ;  in 
a  liquid  the  atoms  are  similar  and  less  closely  packed  ;  while 
in  a  gas  there  are  but  few  atoms  and  they  have  considerable 
freedom  of  motion. 

2.  Atoms  are  imperishable,  of  a  finite  number  of  different 
shapes,  each  shape  being  infinite  in  number. 

3.  The  atoms  are  always  in  motion  and  move  through 
space  at  a  greater  speed  than  sunlight. 

4.  The  properties  of  substances  depend  upon  the  manner 
in  which  the  atoms  combine. 

During  the  seventeenth  century  the  atomic  conception  of 


38  PHYSICAL   CHEMISTRY 

the  composition  of  matter  was  very  popular  and  was  em- 
ployed by  Bacon,  Boyle,  Hooke,  and  others.  Newton 
showed  that  Boyle's  law  of  gases  must  necessarily  follow 
from  this  assumption. 

The  two  Irish  chemists,  Bryan  Higgins  (1737-1820)  and 
his  nephew  and  pupil,  William  Higgins  (1765-1825),  were 
among  the  first  to  seek  quantitative  relation  between  the 
atoms  and  to  attempt  to  determine  the  number  of  atoms 
which  combined  to  produce  a  new  compound.  They  con- 
cluded that  combinations  took  place  most  readily  between 
the  single  ultimate  particles  of  two  substances,  and  William 
Higgins  emphasized  the  law  of  multiple  proportions,  and 
also  the  greater  stability  of  the  products  formed  by  the  union 
of  these  single  particles  (atoms). 

These  views  are  substantially  the  same  as  those  formu- 
lated later  by  Dalton,  as  early  as  1803.  The  Daltonian 
Atomic  Theory  was  based  on  facts  obtained  by  experiment 
and  was  Dal  ton's  method  of  explaining  these  weight  relations 
that  he  had  obtained. 

Dal  ton's  Atomic  Theory  is  stated  as  follows : 

1.  Atoms  are  the  smallest  ultimate  particles  attainable 
and  therefore  cannot  be  subdivided  by  any  known  chemical 
means. 

2.  An  elementary  substance  is  composed  of  an  enormous 
number  of  these  particles,  called  atoms,  which  are  of  the 
same  kind  and  equal  in  weight. 

3.  Atoms  of  different  elements  have  different  properties, 
such  as  weight,  affinity,  etc. 

4.  Chemical  compounds  are  formed  by  the  union  of  the 
atoms  of  different  elements  in  the  simplest  numerical  pro- 
portions. 

In  1808,  Dalton  in  his  statement  of  the  atomic  theory 
emphasized  how  important  it  is  to  be  able  to  arrive  at  a 
knowledge  of  the  relative  weights  of  these  ultimate  particles 
which  combine  to  form  compounds,  and  that  these  relative 


ATOMIC  AND   MOLECULAR  THEORIES  39 

weights  serve  as  a  guide  in  obtaining  the  composition  of 
other  substances.  These  relative  weights  he  collected  in 
1803  in  what  was  termed  a  Table  of  Atomic  Weights. 

Dal  ton  considered  atoms,  the  ultimate  particles  of  com- 
pounds, as  the  ultimate  particles  of  elementary  substances. 
He  assumed  for  example  that  one  atom  of  hydrogen  unites 
with  one  atom  of  oxygen  to  produce  one  atom  of  water. 
In  the  development  of  these  atomic  weight  relations  many 
discrepancies  arose  which  were  difficult  to  reconcile.  Gay 
Lussac  presented  his  Law  of  Combining  Proportions  by 
Volume  (about  1 801-08),  which  is,  that  the  weights  of  equal 
volumes  of  gaseous  substances  are  proportional  to  their 
combining  weights  or,  as  Dal  ton  called  them,  atomic 
weights. 

It  has  been  shown  that  definite  quantities  by  weight  of 
certain  substances  called  elements  unite  to  form  new  sub- 
stances termed  compounds ;  it  has  further  been  demon- 
strated that  when  one  element  combines  with  another  in 
two  or  more  different  ratios  forming  different  substances, 
the  quantities  of  the  first  element  combining  with  a  unit 
quantity  of  the  second  are  in  simple,  integral  ratios.  It  has 
further  been  shown  by  Gay  Lussac,  and  has  subsequently 
been  confirmed,  that  when  reacting  gaseous  elements  com- 
bine, the  volumes  of  the  different  gases  under  the  same  con- 
ditions of  pressure  and  temperature  are  in  simple  ratios  to 
one  another  and  to  the  resulting  gaseous  product.  The 
following  facts  will  serve  as  examples : 

I.  i.  The  combination  of  one  volume  of  chlorine,  bromine,  or  iodine 
with  one  volume  of  hydrogen  to  form  two  volumes  of  the  re- 
sulting compound. 

2.  The  combination  of  one  volume  of  chlorine  with  one  volume  of 
iodine  to  form  two  volumes  of  the  resulting  compound. 

3.  The  substitution  of  chlorine,  bromine,  iodine,  fluorine,  and 
cyanogen  in  many  organic  compounds  are  reactions  of  equal 
volumes. 


40  PHYSICAL   CHEMISTRY 

II.  i.  The  combination  of  one  volume  of  oxygen,  or  one  volume  of  the 
vapor  of  sulphur  or  selenium,  with  two  volumes  of  hydrogen  to 
produce  two  volumes  of  the  resulting  product. 

2.  The  combination  of  one  volume  of  oxygen  with  two  volumes  of 
chlorine. 

3.  The  combination  of  one  volume  of  oxygen  with  two  volumes  of 
nitrogen. 

III.    i.  The  combination  of  one  volume  of  nitrogen  with  three  volumes 

of  hydrogen  to  form  two  volumes  of  the  resulting  product. 
2.  The  combination  of  one  volume  of  nitrogen  with  three  volumes 
of  chlorine. 

As  illustrated  above,  if  a  definite  volume  of  hydrogen 
combines  with  chlorine,  it  has  been  shown  experimentally 
that  this  volume  of  chlorine  is  the  same,  under  the  same 
conditions  of  temperature  and  pressure,  as  that  occupied  by 
the  hydrogen  with  which  it  combined.  We  have  seen  that  the 
law  of  combination  by  weight  holds  true  and  that  it  is  abso- 
lutely exact.  There  must,  therefore,  be  some  weight  rela- 
tion existing  between  these  volume  relations,  since  they 
combine  with  one  another  in  such  simple  integral  ratios. 
If  we  take  the  quantity  of  oxygen  that  is  equivalent  to  the 
arbitrarily  selected  amount  of  our  arbitrarily  selected  Unit 
of  Reference,  and  the  same  volume  of  hydrogen  under  the 
same  conditions  of  temperature  and  pressure,  we  shall  find 
that  the  oxygen  weighs  15.88  times  as  much  as  the  hydrogen. 
If  we  take  16  g.  of  oxygen,  the  same  volume  of  hydrogen  will 
weigh  i  .008  g.  This  same  volume  of  chlorine  weighs  35.45  g. 
and  the  same  volume  of  nitrogen  weighs  14.0  g.,  it  being 
understood  that  the  volumes  are  under  the  standard  condi- 
tions of  temperature  and  pressure.  It  will  be  recalled  that 
these  numbers  are  the  same  as  those  representing  the  symbol 
weights  of  the  elements  hydrogen,  chlorine,  and  nitrogen. 

If  we  take  the  quantities  of  gaseous  elements  equivalent 
to  these  weights,  called  by  Dalton  atomic  weights,  the 
volumes  which  these  occupy  under  the  same  conditions  of 
temperature  and  pressure  will  be  the  same.  Dalton  con- 


ATOMIC  AND   MOLECULAR  THEORIES  41 

eluded  that  in  equal  volumes  of  different  gases  at  the  same 
temperature  and  pressure  there  were  not  the  same  number  of 
ultimate  particles.  Gay  Lussac  showed  that  the  combining 
weights  (or  some  multiple)  of  different  substances  were  pro- 
portional to  their  densities.  In  1811  Avogadro  accepted 
this  law  of  Gay  Lussac  and  concluded  that  the  number  of 
"  integral  molecules  "  in  equal  volumes  of  all  gases  is  the  same 
for  the  same  temperature  and  pressure.  Avogadro  insisted 
that  if  we  were  to  assume  the  molecules  of  elementary  gases 
identical  with  the  atoms,  the  volumetric  relations  could  not 
be  explained,  as  it  would'necessitate  the  subdivision  of  some 
of  the  atoms.  It  was  this  particular  feature  which  met 
with  such  marked  opposition  from  Dalton  and  his  contem- 
poraries and  at  that  time  prevented  the  acceptance  of  Avo- 
gadro's  hypothesis.  Hence  the  existence  of  small  particles 
of  two  different  orders,  the  molecules  and  the  atoms,  as  advo- 
cated by  Avogadro,  received  little  notice  and  the  revival  of 
the  idea  by  Ampere  in  1814  did  not  succeed  in  having  it 
accepted. 

For  the  next  forty  or  fifty  years  a  rather  chaotic  condition 
prevailed,  and  very  little  progress  was  made  in  the  develop- 
ment of  a  system  of  atomic  weights.  In  1860  a  conference 
of  chemists  met  at  Karlsruhe  for  the  purpose  of  discussing 
the  subject  and  eliminating  the  confusion  arising  from  the 
use  of  the  four  systems  of  atomic  weights  then  in  use.  These 
methods  were  that  of :  (i)  Dalton,  based  on  weight  relations 
and  chemical  analysis  ;  (2)  Berzelius,  based  partly  on  chemi- 
cal analysis,  partly  on  physical  principle  (the  Law  of  Iso- 
morphism) and  partly  on  the  Law  of  Combining  Propor- 
tions by  Volume,  all  of  which  did  not  differentiate  between 
atom  and  molecule ;  (3)  Gmelin's  weight  method ;  and 
(4)  Gerhardt  and  Laurent's  method,  in  which  a  realization 
of  Avogadro's  hypothesis  was  manifest,  and  had  a  far- 
reaching  effect.  The  work  of  Cannizzaro,  in  1858,  revolu- 
tionized the  atomic  weight  methods  by  making  Avogadro's 


42  PHYSICAL  CHEMISTRY 

hypothesis  the  basis  of  his  system  ,and  thus  established 
our  modern  system  of  atomic  weights.  This  work  was 
brought  to  the  attention  of  those  chemists  while  in  session  at 
Karlsruhe. 

It  was  by  affirming  the  universal  applicability  of  Avo- 
gadro's  supposition  that  Cannizzaro  stated  that  results  are 
obtained  which  are  in  keeping  with  certain  formulated  laws 
of  chemistry  and  physics.  Avogadro's  method  of  deter- 
mination of  molecular  weights,  which  had  been  practically 
abandoned,  was  revived  by  Cannizzaro,  who  changed  the 
unit  to  which  vapor  densities  were  referred  and  restated  it  as 
follows  :  "  Instead  of  taking  for  your  unit  the  weight  of  an 
entire  molecule  of  hydrogen,  take  rather  the  half  of  this 
weight,  that  is  to  say,  the  quantity  of  hydrogen  contained 
in  a  molecule  of  hydrochloric  acid." 

By  using  the  hypothesis  of  Avogadro,  Cannizzaro  ex- 
amined the  relative  weights  of  compounds,  the  composition 
of  which  he  determined,  and  described  his  method  in  the  fol- 
lowing exact  terms :  "If  the  body  is  a  compound,  it  is 
analyzed  and  the  constant  weight-relations  of  its  constituents 
are  determined ;  the  molecular  weight  is  then  divided  into 
parts  proportional  to  the  relative  weights  of  the  compounds, 
and  the  result  is  the  quantities  of  the  elements  contained  in 
the  molecule  of  the  compound,  referred  to  the  same  unit 
(namely,  the  semi-molecule  of  hydrogen)  as  is  used  for  the 
expression  of  all  molecular  weights." 

Cannizzaro 's  law  of  atoms  has  made  it  possible  to  express 
the  composition  of  molecules  in  terms  of  their  constituent 
atoms,  for  all  gaseous  and  gasifiable  compounds,  and  was 
stated  by  him  as  follows : 

By  comparing  the  different  quantities  of  one  and  the  same 
element  which  are  contained,  either  in  the  molecules  of  the 
free  elements,  or  in  the  molecules  of  its  compounds,  the  fol- 
lowing law  stands  out  in  relief  :  "  The  different  weights  of  one 
and  the  same  element  contained  in  the  various  molecules  are 


ATOMIC  AND   MOLECULAR  THEORIES  43 

always  whole  multiples  of  one  quantity,  which  is  justly  called 
the  atom,  because  it  invariably  enters  the  compounds  without 
division." 

The  atom  of  an  element,  Cannizzaro  said,  "  is  expressed 
by  that  quantity  of  it  which  invariably  enters  as  a  whole 
into  equal  volumes  of  the  simpler  substance  and  its  com- 
pounds ;  this  quantity  may  be  either  the  whole  quantity  con- 
tained in  a  volume  of  the  free  element  or  a  fraction  thereof." 
However,  "  In  order  to  determine  the  atomic  weights  of  any 
element  it  is  essential  to  know  the  molecular  weights,  and 
the  compositions,  of  all  or  most  of  its  compounds." 

We  then  have  described  by  Cannizzaro  a  clear  picture 
of  the  interrelations  of  all  the  fundamental  conceptions  of 
Dalton  and  Avogadro,  which  were  at  their  time  practically 
discarded ;  in  this  way  there  was  developed  a  complete 
theory  which  "  placed  the  atomic  weights  of  the  metallic 
elements  on  their  present  consistent  bases."  Cannizzaro 
thus  advanced  the  theory  of  atomic  equivalency,  which  em- 
phasized "  the  unchangeability  of  the  proportions  between 
the  atomic  weights  of  the  bodies  which  usually  replace  one 
another,  whatever  be  the  nature  and  number  of  the  other 
constituents  of  the  compounds."  This  is  a  law  which  limits 
the  number  of  possible  compounds  and  more  especially 
applies  to  all  cases  of  double  exchange. 

THE  MOLECULAR  THEORY 

This  is  the  method  for  the  determination  of  the  combin- 
ing or  atomic  weights  which  is  employed  at  the  present  time, 
and  which  is  illustrated  in  the  following  consideration : 

For  chemical  reasons,  chemists  have  accepted  Avogadro's 
hypothesis,  which  leads  to  the  molecular  structure  of  matter. 
This  hypothesis,  known  as  the  Molecular  Theory  of  Matter, 
conceives  matter  as  discontinuous  and  made  up  of  minute 
particles  called  molecules.  The  molecules  of  the  same  sub- 
Stance  are  assumed  to  be  alike  in  all  respects.  The  mole- 


44  PHYSICAL  CHEMISTRY 

cules  are  considered  to  be  practically  independent,  with 
space  between  them,  and  may  be  defined  as  "  that  minute 
portion  of  a  substance  which  moves  about  as  a  whole  so  that 
its  parts,  if  it  has  any,  do  not  part  company  during  the 
excursions  the  molecule  makes  ;  and  the  molecular  weight  is 
the  weight  of  this  ultimate  particle  referred  to  the  weight  of 
the  molecule  of  a  standard  substance." 

As  a  working  hypothesis  this  assumption  of  Avogadro  has 
been  very  fruitful,  as  the  following  illustration  indicates. 

i.  Hydrogen  and  chlorine  unite  to  produce  hydrochloric 
acid. 

Facts.     We  have  determined  experimentally  : 

i  .  Equal  volumes  of  hydrogen  and  chlorine  react  to  pro- 
duce two  volumes  of  hydrochloric  acid. 

Hydrogen       +        Chlorine    =         Hydrochloric  acid 


i  vol.  +  i  vol.       =  2  vols. 

2.  By  analysis  it  has  been  shown  that  hydrochloric  acid 
consists  of  hydrogen  and  chlorine  in  the  ratio  of  one  symbol 
weight  of  hydrogen  to  one  symbol  weight  of  chlorine. 

Assumptions. 

1.  In   unit    volume    let   us    assume    that    there    are    n 
molecules. 

2.  According  to  Avogadro's  assumption  equal  volumes 
contain  an  equal  number  of  molecules. 

Since  there  are  two  volumes  of  hydrochloric  acid,  accord- 
ing to  Avogadro's  hypothesis  this  volume  must  contain  twice 
as  many  molecules  of  hydrochloric  acid  as  there  are  molecules 
of  hydrogen  in  the  one  volume  of  hydrogen.  That  is,  one 
volume  of  hydrogen  contains  n  molecules  of  hydrogen,  and 
two  volumes  of  hydrochloric  acid  contain  2  n  molecules  of 
hydrochloric  acid. 


ATOMIC  AND   MOLECULAR  THEORIES  45 

It  follows  that  the  number  of  atomic  weights  of  hydrogen 
in  2  n  molecules  of  hydrochloric  acid  must  be  the  same  as  in 
the  n  molecules  of  hydrogen. 

If  we  assume,  for  simplicity,  that  each  molecule  of  hydro- 
chloric acid  contains  one  atom  of  hydrogen,  then  2  n  mole- 
cules of  hydrochloric  acid  will  contain  2  n  atoms  of  hydrogen ; 
but  these  2  n  atoms  of  hydrogen  must  have  been  furnished 
by  the  n  molecules  of  hydrogen.  Therefore,  one  molecule 
of  hydrogen  must  contain  at  least  two  atoms  of  hydrogen, 
and  the  formula  is  written  H2,  which  represents  the  molecule 
of  hydrogen.  Similarly  the  molecule  of  chlorine  may  be 
shown  to  contain  two  atoms,  and  its  formula  is  C12. 

By  pursuing  a  course  of  reasoning  analogous  to  the  above, 
it  may  be  shown  that  the  molecules  of  some  other  gaseous 
elements  consist  of  at  least  two  atoms.  By  grouping  the 
symbols  of  the  elements  we  obtain  the  formula  of  the  ele- 
ment which  represents  the  molecular  weight  and  indicates 
the  number  of  atoms  of  each  element  present  in  the  molecule. 


CHAPTER  VI 

DEVIATIONS  FROM  THE   GAS  LAW  AND   DISSOCIATION 
OF  GASES 

IT  has  already  been  stated  that  only  for  ideally  perfect 
gases  does  the  Gas  Law  Equation  hold,  but  in  the  case  of 
O2,  N2,  H2,  and  air  the  deviations  are  so  small  for  moderate 
ranges  of  pressure  and  temperature  that  they  conform  to 
the  laws  very  closely  and  therefore  may  be  considered  for 
all  practical  purposes  as  perfect  gases.  Although  these  de- 
viations are  small,  they  are  real,  and  there  must  be  certain 
causes  which  produce  these  deviations  from  the  theoretical 
laws. 

Deviation  from  Boyle's  Law.  —  If  gases  are  subjected  to 
very  high  pressures,  the  change  in  volume  does  not  conform 


too 


FIG.  2. 

to  Boyle's  Law :  Vo :  V :  :  p :  po,  or  Vo  X  po  =  Vp,  or  Vp 
=  constant.  Or,  expressed  graphically,  we  would  have  the 
curve  as  represented  in  Fig.  2. 

But  the  experimental  results  of  Amagat  on  the  effects 
of  high  pressure  show  that  the  value  of  p  V  is  not  a  con-. 
stant  for  different  pressures,  and  this  is  illustrated  by  the 
data  given  in  Table  II. 

46 


DEVIATIONS   FROM  THE  GAS  LAW 
TABLE  II  —  Value  of  pV  at  o°  C. 


47 


p 

HYDROGEN 

ATP 

CARBON 

IjTH  YL  EN  E 

IN  ATM. 

t\lR 

DIOXIDE 

100 

.069 

0.9265 

0.9910 

0-973 

0.2O2O 

0.310 

2OO 

.138 

0.9140 

1.039 

I.OIO 

0.385 

0.565 

300 

.209 

0.9624 

1.136 

1.097 

0-559 

0.806 

500 

.3565 

1.1560 

1.390 

1.340 

0.891 

1.256 

700 

•504 

1.385 

1.662 

1.602 

1.  206 

1.684 

IOOO 

.7200 

1.7350 

2.068 

1.992 

1.656 

2.289 

15-4°  C. 

15.6°  C. 

1  6°  C. 

15-7°  C. 

1000 

1.893 

1.800 

2.134 

2.062 

1500 

2.240 

2.357 

2.8995 

2.661 

2000 

2.562 

2.888 

3.398 

3.286 

2500 

2.870 

3-375 

3-990 

3.855 

3000 

3.162 

3.888 

4.569 

4.398 

These  data  are  represented  graphically  in  Fig.  3. 


Atmos. 


FIG.  3. 


48 


PHYSICAL  CHEMISTRY 


From  Fig.  3  it  is  apparent  that  with  increase  of  pressure 
the  value  of  pV  first  decreases,  reaches  a  minimum,  and  then 
increases,  except  in  the  case  of  hydrogen,  where  we  have 
only  the  portion  of  the  curve  representing  an  increase  in  the 
value  of  pV,  which  led  Regnault  to  call  hydrogen  a  "  more 
than  perfect  gas,"  because  the  volume  was  not  decreased  as 
much  as  it  should  be  according  to  Boyle's  Law.  That  por- 
tion of  the  curve  of  all  gases  which  represents  the  high  pres- 
sure shows  that  the  gases  are  not  compressed  as  much  as 
they  should  be  according  to  Boyle's  Law. 

Confirmation  of  these  results  is  found  in  the  work  of  Wit- 
kowski,  Kamerlingh  Onnes  and  Brook,  Ramsay  and  Young, 

Barus,  and  others.  The  change 
of  the  value  of  p  V  with  the  change 
in  p  at  various  temperatures  has 
been  obtained  by  these  workers, 
and  this  is  illustrated  in  Fig.  4. 

It  appears,  then,  that  there  must 
be  a  particular  temperature  for 
each  gas  at  which  the  depression 
in  the  isothermal  just  disappears, 
so  that  it  is  horizontal  through  a 
considerable  range  of  pressures. 
At  this  temperature  a  gas  follows 
Boyle's  Law  exactly,  up  to  a  fairly 
high  pressure,  and  behaves  to  this 
extent  like  an  ideal  or  perfect  gas. 
This  is  also  true  for  a  short  dis- 
tance at  and  near  the  minimum 
value  for  pV,  while  at  the  high 
pressures  the  isotherms  approxi- 
mate nearly  parallel  straight  lines. 
Low  Pressures.  —  In  the  case  of  very  low  pressures,  there 
is  not  so  marked  a  variation,  and  the  conformity  to  Boyle's 
Law  is  more  marked.  Experimentation  along  this  line  has 


100  ZOO 

Pressure  In- Atmosphere 

FlG.   4. 


DEVIATIONS  FROM  THE   GAS  LAW  49 

been   carried   out   by   Mendeleeff,    Amagat,    Ramsay  and 

Barly,  Battelli,  Rayleigh,  Regnault,  Leduc,  and  others.  The 

conclusion  from  their  work  is  that  in  the  equation  ^  =  b, 


where  V  is  the  larger  volume  and  p  is  the  smaller  pressure, 
the  value  of  b  approaches  and  finally  reaches  unity  as  the 
pressure  falls.  In  the  case  of  hydrogen  the  value  rises,  and 
for  other  gases  it  falls.  For  the  range  of  pressures,  of  75  to 
150  mm.  the  differences  from  unity  are  quite  negligible  in 
the  cases  of  hydrogen,  air,  and  probably  nitrogen.  There  is 
a  slight  difference  in  the  case  of  oxygen,  but  this  difference 
disappears  at  still  lower  pressures.  For  N2O  the  value  of  b 
is  fairly  high  between  75  and  150  mm.  The  following  are 
the  values  of  b  obtained  by  Rayleigh  : 

b 
Air     .......     .....    0.99997 

H2      ............     0.99997 

O2       ............     1.00024 

Argon      ...........     1.00021 

N2O    .     ...........     1.00066 

While  the  deviations  from  Boyle's  Law  are  apparent,  they 
are  so  small  at  low  pressures  that  they  are  difficult  to  detect, 
even  by  very  accurate  experiments,  yet  they  prove  that  these 
gases  do  not  follow  Boyle's  Law  absolutely. 

Deviation  from  Charles'  or  Gay  Lussac's  Law.  —  The  co- 
efficient of  expansion  of  gases  varies  with  a  change  of  tem- 
perature and  pressure.  This  is  emphasized  in  the  case  of 
ethylene  in  Table  III,  taken  from  Amagat's  data. 

The  pressure  remaining  constant,  the  horizontal  lines  in 
Table  III  show  a  variation  of  the  coefficient  of  expansion  with 
the  change  of  temperature.  There  is  no  regularity  in  the 
change,  but,  in  general,  at  higher  temperatures  the  variation 
is  less  than  at  lower  temperatures.  The  vertical  columns 
show  a  marked  decrease  in  the  coefficient  of  expansion  with 
increased  pressure.  The  minimum  value  of  the  coefficient 


PHYSICAL   CHEMISTRY 


of  expansion  corresponds  closely  with  the  minimum  values 
for  pV. 

TABLE  III  —  COEFFICIENTS  OF  EXPANSION  OF  ETHYLENE 


PRESSURE 
METERS  OF 
MERCURY 

3o0-4o° 

40°-SO° 

6o°-8o° 

8o°-ioo° 

30 

.0084 

.0064 

.0646 

.0040 

60 

.0166 

.0178 

.0097 

.0067 

80 

.OI2I 

.0195 

.0132 

.0088 

IOO 

.0079 

.0108 

.0121 

.OIOO 

I2O 

.OO62 

.0075 

.0095 

.0082 

I4O 

.0048 

.0062 

.0076 

0068 

1  6O 

.0041 

.0057 

.0061 

.0058 

2OO 

.0034 

.0043 

.0044 

.0044 

240 

.0030 

•0035 

.0036 

•0034 

280 

.0027 

.0031 

.0030 

.0029 

320 

.0025 

.0027 

.0024 

.0024 

This  is  in  confirmation  of  the  results  of  Regnault,  who 
showed  that  no  gas  is  really  perfect,  but  he  concluded  that 
the  coefficients  for  different  gases  become  more  and  more 
nearly  equal  as  the  pressure  falls,  and  that  the  statement  that 
the  coefficients  are  equal  may  be  taken  as  correct  only  for 
very  low  pressures. 

The  relations  of  the  coefficient  of  expansion  and  the  co- 
efficient of  increase  of  pressure  are  given  in  Table  IV,  com- 
piled by  Young.  At  constant  pressure,  Vt  =  VQ(I  +  a/), 
where  a  is  the  coefficient  of  expansion ;  at  constant  vol- 
ume, pt  =  po(i  +  (3t),  where  ft  is  the  coefficient  of  increase 
of  pressure  and  p  is  the  constant  pressure  at  which  a  was 
determined,  and  p0  the  initial  pressure  in  the  determina- 
tions of  /3. 

Gay  Lussac  believed  that  all  gases  had  the  same  coefficient 
of  expansion  at  constant  pressure  and  that  this  was  1/273 
or  0.0036675  of  the  original  volume  at  o°  C.  and  under  a 
pressure  of  one  atmosphere,  and  since  they  obeyed  Boyle's 


DEVIATIONS   FROM  THE   GAS  LAW 


Law  they  therefore  all  had  the  same  coefficient  of  increase 
of  pressure  (|3)  at  constant  volume,  i.e.  a  =  (3. 

TABLE  IV 


GAS 

OBSERVER 

(o°-"oo°) 

P 

ft 
(o°-ioo°) 

Hydrogen       .     . 

Regnault 

0.003661 

i  atmos. 

0.003668 

Hydrogen       .     . 

Chappuis 

0.00366004 

i  meter 

0.00366254 

Hydrogen       .     . 

K.  Onnes  and  Bondin 

i  meter 

0.0036627 

Hydrogen       .     . 

Richards  and  Marks 

0.0036609 

Hydrogen       .     . 

Travers  and  Jaquerod 

700  mm. 

0.00366255 

Hydrogen       .     . 

Travers  and  Jaquerod 

500  mm. 

0.0036628 

Helium       .     .     . 

Travers  and  Jaquerod 

700  mm. 

0.00366255 

Helium       .     .     . 

Travers  and  Jaquerod 

500  mm. 

0.0036628 

Nitrogen    .    .     . 

Regnault 

i  atmos. 

0.003668 

Nitrogen    .     .     . 

Chappuis 

0.00367313 

i  meter 

0.0036744 

Nitrogen    .     .     . 

Chappuis 

530.8  mm. 

0.0036638 

Air 

Regnault 

0.003671 

i  atmos. 

0.003665 

Oxygen 

Makower  and  Noble 

mean  values 

663.38  mm. 

0.0036738 

Oxygen       .     .     . 

Makower  and  Noble 

353.99  mm. 

0.0036698 

Carbon  monoxide 

Regnault 

0.003669 

i  atmos. 

0.003667 

Carbon  dioxide 

Regnault 

0.003710 

i  atmos. 

0.003688 

Carbon  dioxide 

Richards  and  Marks 

0.0037282 

Sulphur  dioxide 

Regnault 

0.003903 

i  atmos. 

0.003845 

Nitrous  oxide 

Regnault 

0.003719 

i  atmos. 

0.003676 

ft  (o°-io67°) 

Nitrogen    .     .     . 

Jaquerod  and  Perrot 

240 

0.0036643 

Air    

Jaquerod  and  Perrot 

230 

0.0036643 

Oxygen       .     .     . 

Jaquerod  and  Perrot 

180-230 

0.0036652 

Carbon  monoxide 

Jaquerod  and  Perrot 

230 

0.0036648 

Carbon  dioxide 

Jaquerod  and  Perrot 

240 

0.0036756 

Carbon  dioxide 

Jaquerod  and  Perrot 

170 

0.0036713 

Chappuis  found  as  the  average  of  the  values  for  the  co- 
efficient of  expansion  of  nitrogen  0.00366182,  and  Berthelot 
found  for  the  values  of  hydrogen:  0.00366248,  0.00366206, 
and  0.00366169.  The  mean  of  the  values  of  nitrogen  and 

hydrogen  gives  0.00366193,  or 


273.080' 


i.e.   a  = 


273.1 


or 


o°  C.  =  273.1°  absolute. 


These  variations  from  the   laws  of   Boyle  and  of   Gay 
Lussac  are  but  slight  in  the  case  of  those  gases  which  are 


52  PHYSICAL   CHEMISTRY 

difficult  to  liquefy,  such  as  hydrogen,  nitrogen,  air,  oxygen, 
etc.,  but  the  variations  are  very  pronounced  in  the  case  of 
those  which  are  readily  liquefiable,  such  as  sulphur  dioxide, 
carbon  dioxide,  ethylene,  etc.  Various  efforts  have  been 
made  to  explain  these  variations  from  The  Gas  Law,  which 
we  have  seen  show  that  at  low  pressures  some  gases  are  too 
compressible,  while  under  high  pressure  they  are  not  com- 
pressible enough.  Among  the  most  fruitful  of  the  expla- 
nations offered  is  the  one  of  van  der  Waals.  There  is  an- 
other type  of  variation  from  The  Gas  Law  in  the  case  of 
certain  other  gases  which  give  abnormal  values  for  the  den- 
sity with  increased  temperature.  This  variation  is  explained 
upon  the  supposition  that  the  gas  molecules  are  dissociated 
with  the  formation  of  new  chemical  individuals. 

VARIATIONS  FROM  THE  GAS  LAW  AS  EXPLAINED  UPON  THE 
BASIS  OF  DISSOCIATION  OF  THE  GAS 

Attention  has  been  called  to  the  fact  that  a  number  of 
substances  do  not  conform  to  the  Gas  Law  Equation  and 
that  the  vapor  density  determinations  give  abnormal  values 
for  the  molecular  weights.  It  was  recognized  by  the  ear- 
lier workers  that  the  results  must  be  due  to  abnormal 
molecular  conditions  and  that  Avogadro's  hypothesis  did 
not  hold  for  these  cases,  such  as  ammonium  chloride,  phos- 
phorus pentachloride,  nitrogen  dioxide,  etc.  Almost  simul- 
taneously Cannizzaro  (1857),  Kopp  (1858),  and  Kekule* 
(1858)  advanced  the  idea  that  these  abnormal  values  were 
due  to  the  decomposition  of  the  substance.  This  decom- 
position was  termed  dissociation  by  St.  Claire  Deville  (1857). 
This  assumption  of  the  dissociation  of  the  gaseous  mole- 
cules to  account  for  the  low  density  was  not  readily 
accepted,  and  it  devolved  upon  the  champions  of  the  idea  to 
prove  that  dissociation  did  take  place. 

The  following  four  typical  examples  were  employed  to 
prove  the  dissociation  of  these  substances : 


DEVIATIONS   FROM  THE   GAS  LAW  53 

1 .  Deville  found  on  raising  the  temperature  of  PC15  that  at 
high  temperatures  the  colorless  gas  became  decidedly  green. 
This  may  be  explained  by  the  following  equation  :  PC15  =  PCla 
-f  C12 ;  the  green  color  being  due  to  the  chlorine  gas  present. 

2.  On  heating  N2O4,  which  is  colorless,  it  becomes  dark 
brown,  and  on  cooling  it  decolorizes  again.     Salet  showed 
(1868)  that  the  color  varied  with  the  vapor  density.     Under 
high  pressures  approximately  normal  densities  for  N2O4  are 
obtained,   while  at  high  temperatures  and  low  pressures, 
values  approximating  that  of  NO2  are  obtained,  and  hence 
we  conclude  that  the  brown  color  is  due  to  NO2. 

3.  Pebael  heated  ammonium  chloride  which  had  been 
incorporated  in  an  asbestos  plug.     During  the  heating  a 
current  of  air  was  passed  through  the  tube.     By  means  of 
litmus  paper  he  proved  that  an  excess  of  hydrochloric  acid 
was  present  in  one  end  of  the  tube,  while  at  the  other  end 
ammonia  was  in  excess.     Thau  used  nitrogen  instead  of  air, 
and  by  a  slight  modification  of  the  method  confirmed  the 
dissociation  of  ammonium  chloride. 

4.  In  the  case  of  chloral  hydrate,  Toost  proved  that  the 
low  density  was  due  to  dissociation  by  distilling  chloral 
hydrate  (melting  point  57°  C.),  and  collecting  its  vapor  in 
chloroform.     Chloral   dissolves   but   the   water   does   not ; 
hence  he  concluded  that  the  chloral  hydrate  was  dissociated 
according  to  the  equation 

CC13  •  CH(OH)2  =  CC13  •  CHO  +  H2O. 

The  presentation  of  these  data  soon  resulted  in  the  general 
acceptance  that  dissociation  was  the  cause  of  the  abnormal 
values  of  the  densities. 

One  of  the  common  applications  of  dissociation  is  made 
use  of  in  cleaning  the  soldering  iron  by  rubbing  it  against 
solid  ammonium  chloride,  the  liberated  hydrochloric  acid 
acting  as  the  cleaning  agent.  Commercial  hydrochloric 
acid  is  now  used  extensively  for  that  purpose. 


54  PHYSICAL  CHEMISTRY 

Degree  of  Dissociation.  — 

Let  a.  =  degree  of  dissociation  or  per  cent  dissociation 

n  =  number  of  molecules 
/  =  number  of  parts  into  which  each  molecule  is  disso- 

ciated 

then  an  =  number  of  molecules  dissociated 
n  —  an  =  number  of  molecules  undissociated 

anf  =  number  of  parts  resulting  from  dissociated  molecules 
n  —  an  +  anf  =  total  number  of  parts  or  molecules  after  dissociation. 
Let  i  denote  the  ratio  of  the  number  of  molecules  after  dissociation 
to  the  number  of  molecules  before  dissociation, 

Then          i  =  n-cin+anf  OT  l  _  a  +  a  l 


That  is       i  =  I  +  (/  -  i)a  or  a  =  -*-=-^  (2) 

Let  p  =  density  before  dissociation 

Pi  =  density  after  dissociation 
V  =  volume  before  dissociation 
Vi  =  volume  after  dissociation 
n  =  number  of  molecules  before  dissociation 
n  —  an  +  anf  =  number  of  molecules  after  dissociation. 

Since         ,  = 


mass 
and*- 


From  Avogadro's  Hypothesis        =  n  ~  an  +  anf 


Substituting  we  have  £  =  n  ~  an  +  anf  =  !-«+«/ 

pi  n 

and  solving  for  a  we  have  a  =    P~Pl-  (3) 

Pi(f-  0 

If  5  is  the  specific  gravity  before  dissociation  and  5i  the 
specific  gravity  after  dissociation,  then  from  page  5,  p  =  sps 
and  pi  =  Sips.  Substituting  in  formula  (3)  we  have 

Sps  —  Sips  S  —  Si 

r'       ^    or    «  - 


slPs(f-i) 


DEVIATIONS   FROM  THE   GAS  LAW  55 

_p 

If  *  =  ^,we  have  «  =  —  £  -  ^^  =  k. 

rj          / 

That  is,  the  degree  of  dissociation  is  complete,  or  100  per 
cent. 

If  a  substance  dissociates  into  2  parts,  its  vapor  density 

Pi  =  -,  that  is,  £  of  original  density.     If  into  3  parts,  pi  =  - 
2  3 

that  is,  \  of  its  original  density.     But  if  pi  =  p,  then  a  =  o 
and  no  dissociation  takes  place. 

EXAMPLE.  —  At  90°  C.  the  specific  gravity  of  nitrogen  peroxide 
(N2O4)  is  24.8  (H  =  i).     Calculate  degree  of  dissociation. 


''•  a  =  J/"-*)  =  2^8  7/-  i)  =  °'8547  ''  •'•  8547  per  cent  dissociated. 

EXAMPLE.  —  When  5  g.  of  ammonium  carbamate  NH4CO2NH2 
are  completely  vaporized  at  200°  C.,  it  occupies  a  volume  of  7.66  liters 
under  a  pressure  of  740  mm.  mercury.  Calculate  the  degree  of  dissocia- 
tion. 

2  NH3  +  CO2 

m  =  78,  molecular  weight  of  ammonium  carbamate 

-£-  —  gram-molecules  =  -5- 
m  78 


(i  +  2  a)—  =  total  number  of  molecules 
m 

pV  =  nRT:       pV  =  -£-(1  .+  2  a)tfr;  />  =  74?  atmosphere 
w  760 

24°.  x  7-66  =  -^  (i  +  2  a)  X  0.082  X  473. 
700  78 

Solving,  find    a  =  0.999  °r  99-9  per  cent  dissociation. 


56  PHYSICAL   CHEMISTRY 

On  complete  dissociation,  we  have  in  the  case  of  nitrogen 
peroxide  a  simple  gas,  while  in  the  case  of  ammonium  car- 
bamate  we  have  a  gaseous  mixture  consisting  of  ammonia 
and  carbon  dioxide.  Depending  upon  the  temperature  and 
pressure  we  have,  in  all  intermediate  states,  partial  dissocia- 
tion. We  see  that  certain  gaseous  substances  which  give 
abnormal  values  for  their  densities,  upon  the  basis  that  they 
are  dissociated,  confirm  Avogadro's  hypothesis,  and  that 
the  state  of  an  ideal  gas  is  realized  when  there  is  complete 
dissociation,  as  in  the  case  of  the  undissociated  gases  we  have 
previously  considered. 

The  Law  of  Mass  Action.  —  In  the  type  of  reactions  we 
have  been  discussing,  at  ordinary  temperatures  and  pressures 
the  substances  nitrogen  dioxide  and  ammonium  carbamate 
are  distinct  chemical  individuals,  the  one  a  gas  and  the  other 
a  solid.  If  they  are  heated,  they  dissociate,  with  the  forma- 
tion of  new  chemical  individuals  as  illustrated  in  the  equa- 
tions above.  As  the  temperature  is  increased  more  and 
more,  the  original  substance  is  dissociated,  while  at  any 
specified  temperature  the  products  of  dissociation  are  in 
equilibrium  with  the  undissociated  substance.  The  state  of 
equilibrium  we  represent  by  equations,  such  as  N2O4  ^± 
2  NO2,  which  means  that  the  reaction  may  proceed  in  either 
direction  and  is  designated  a  reversible  reaction ;  but  for 
any  specified  conditions  it  does  proceed  in  both  directions 
at  the  same  rate,  and  consequently  an  equilibrium  is  thus 
maintained.  The  law  governing  the  state  of  equilibrium  or 
this  statical  condition  of  the  reaction  is  known  as  the  Law 
of  Mass  Action  and  can  be  developed  thermodynamically ; 
but  this  particular  theoretical  consideration  of  the  subject 
will  have  to  be  deferred,  and  we  will  illustrate  the 
meaning  of  the  law  by  applying  it  to  a  few  specific 
cases. 

Suppose  we  have  two  substances,  A  and  B,  reacting  to 
form  their  resulting  product,  AB.  Then  A  -f  B  =  AB, 


DEVIATIONS   FROM  THE   GAS  LAW  57 

or  we  may  have  the  reverse,  AB  =  A  +  B,  or  writing  as 
one  equation  we  have  AB  ^±  A  +  B.  A  more  general 
statement  would  be  where  more  substances  react,  forming 
a  homogeneous  system.  The  reaction  is  represented 
thus, 

A1  +  Az  +  A3 -  ^±  AS  +  AJ  +  A3'  ... 

which  indicates  that  only  one  molecule  of  each  substance 
takes  part  in  the  reaction.  That  this  reaction  takes  place 
depends,  according  to  the  kinetic  theory  of  gases,  upon  the 
collision  of  the  molecules,  and  it  is  obvious  that  the  nearer 
they  are  together  the  more  numerous  such  collisions  and  the 
greater  the  relative  number  of  molecules  per  unit  space. 
Hence  the  reaction  (i.e.  collisions)  is  proportional  to  the 
concentration.  Then  the  velocity  of  the  reaction  is  propor- 
tional to  the  products  of  the  concentrations. 

Let  V  =  velocity  from  left  to  right,  and  ci,  c2  •••  represent 
the  concentrations  of  the  substances  A\,  A2  —,  i.e.  the 
number  of  gram-molecules  per  liter.  Then  the  reaction 
equation  is  V  =  KciC2  •••,  where  K  is  a  constant  for  the 
given  temperature. 

If  the  reaction  proceeds  in  the  direction  from  right  to  left, 
we  shall  have  V  =  Kfc\c2  — ,  in  which  the  terms  have 
analogous  meaning  to  those  in  the  first  cases. 

As  the  values  of  V  and  V  cannot  be  measured  alone,  the 
course  of  the  reaction  can  only  be  given  by  the  difference  of 
the  two  values.  The  total  reaction  velocity  is  made  up  of 
the  difference  between  the  two  partial  reacting  velocities ; 
for  the  change  actually  observed  for  any  amount  of  time  is 
equal  to  the  reaction  in  one  direction  minus  the  change  in 
the  opposite  direction  during  this  same  time.  When  the 
condition  of  equilibrium  has  been  reached,  we  are  not  to 
conclude  that  no  further  change  takes  place ;  but  should 
assume  that  the  change,  in  the  sense  of  the  reaction  equation 
from  left  to  right,  is  compensated  by  a  change  from  right  to 


58  PHYSICAL  CHEMISTRY 

left,  and  therefore  that  the  total  change  to  be  observed 
=  zero,  i.e.  the  system  stands  in  equilibrium.  Then  we 
have  for  equilibrium 

V  -  V  =  o,  or  V  =  V 
.'.Kcic2'"  =  K'CI'CZ  '». 

A  more  general  statement  would  be  to  remove  the  restric- 
tion that  only  one  molecule  takes  place  in  the  reaction  and 
that  there  is  only  one  molecule  of  each  molecular  species 
produced.  In  that  case  the  formula  takes  the  following 
form  for  the  Generalized  Mass  Law  Equation  : 


gl*.g.*.  ,.«....      =IC       k  a  Qon 

ci'n*'  •  c2'n3'  •  c3'n3'  -       K 

which  is  termed  the  equilibrium  constant;  but  where  applied 
to  dissociation  phenomena  it  is  termed  the  dissociation 
constant. 

Now  applying  this  Mass  Law  Equation  to  the  simplest 
case  of  dissociation,  when  a  compound  AB  dissociated  into 
the  two  parts  A  and  B,  we  have  AB  ^±  A  +  B, 

(1)  Kci  =  cz  •  cz.     If  the  reacting  substance  is  made  up 
of  like  parts,  then  we  have 

A  i  ^±  2  A  2,  which  becomes 

(2)  Kci  =  C22,  which  is  obtained  from  the  above   when 
c2  =  cz.     That  is,  where  the  substance  dissociates  into  two 
like  constituents. 


Let  c,  the  concentration  =  g/no'  of  L™1™\     Substitut- 

FV        vol.        / 

ing  this  value  for  the  concentration  in  equations  (i)  and  (2) 
we  have 


VJ     V     V 


DEVIATIONS   FROM  THE   GAS   LAW  59 

Now  since  n%  =  n$,  we  have 


which  becomes 


HI 

That  is,  increasing  the  volume  produces  a  relative  increase  of 
dissociation. 

Many  times  it  is  difficult  to  determine  the  concentration  of 
the  components.  We  can  avoid  the  necessity  of  doing  so  by 
introducing  the  pressure  factor  and  measuring  that  instead 
of  determining  tjie  concentration.  The  final  form  of  the 
Gas  Law  Equation  was 

pV  =  nRT  (3) 

which  becomes 


n       p  '        V      RT 

But  since  —  =  c,  we  have  c  =  -*•  — 
V  RT 

The  concentrations  are  directly  proportional  to  the  pres- 
sures. The  equation  then  becomes 

c  =  Idp.  (4) 

Now,  since  concentration  is  proportional  to  the  pressure, 
for  c\  we  may  substitute  K\p  in  the  equations  above,  and  we 
have  for  equation  (2)  Kc\  =  (c22)  the  following 

K(KlPl)  =  (Kzp,Y 
or 


Now  since  K—±  represents  a  new  constant,  we  may  ex- 
press this  by  some  single  letter,  as  k,  hence  we  have  k  =  &-> 


60  PHYSICAL  CHEMISTRY 

This  gives  us  the  pressures  due  to  the  individual  constituents 
of  the  gas  mixture,  and  these  are  designated  the  partial 
pressures.  The  total  pressure  P  is  the  sum  of  the  partial 
pressures,  i.e.  P  =  pi  +  pz.  This  is  Dalton's  Law.  From 
a  consideration  of  The  Gas  Law  we  have,  for  several  molecu- 
lar species  occupying  the  same  volume  at  the  same  tempera- 
ture, the  relation  ^  =  — '• 
p2  nz 

Mixtures  of  Gases.  —  We  should  expect  that  the  most 
simple  relations  would  be  found  to  exist  in  the  case  of  mix- 
tures of  different  gases.  Such  is  the  case  where  there  is  no 
chemical  action  between  the  gaseous  particles.  Each  gas 
remains  unchanged  and  conducts  itself  as  though  the  other 
one  was  not  present.  The  pressure  exerted  upon  the  walls 
of  the  containing  vessel,  the  capacity  of  absorbing  and  re- 
flecting light,  the  specific  heat,  etc.,  in  fact  all  of  the  proper- 
ties of  the  gases  experience  no  change  when  the  gases  are 
mixed.  These  particular  relations  should  hold  only  in  the 
case  of  ideal  gases ;  and  as  all  the  gases  only  approximately 
follow  The  Gas  Law,  we  should  expect  to  find  some  slight 
deviations  when  the  gases  are  mixed. 

Dissociation  of  Gases.  —  Let  us  consider  the  following 
cases : 

(i)    PC15  ^±  PC13  +  C12    and     (2)    2  HI  ^±  H2  +  I2. 
Applying  the  mass  law,  we  have 

Kci  =  c2  •  c3.  Kci2  =  c2  -  c3. 

Expressing  concentrations  in  terms  of  number  of  mole- 
cules in  unit  volume,  we  have 

7^wi_=tt2     nj  x^  =  ^     ^ 

V    .V.  V  V2      V  '  V* 

Multiplying  through  by  V,  and  by  V2, 

Kn,  =  25-  Km2  =  n,  •  n3. 


DEVIATIONS   FROM  THE   GAS  LAW  6l 

In  the  case  of  PC15  the  dissociation  is  proportional  to  the 
volume,  while  in  HI  as  there  is  no  value  of  V  in  the  equa- 
tion, the  dissociation  is  independent  of  the  volume. 

Introducing  the  pressures  instead  of  the  concentrations 
we  have 

Kipi  =  p2  -  pi.  KipS  =  p2  •  p». 

We  can  decrease  the  volume  by  increasing  the  pressure 
m-fold,  when  we  shall  have 


which  become 

Kipi  =  p2  •  mpz.  Kipi2  =  p2  -  p3. 

In  the  first  case  we  have  the  dissociation  forced  back, 
while  in  the  other  case  it  is  not  affected  by  the  increase  of 
pressure,  as  the  factor  m  disappears.  Hence,  in  all  cases 
where  the  number  of  reacting  substances,  i.e.  the  number  of 
molecules  on  both  sides  of  the  equation,  are  equal,  the  change  in 
the  volume  has  no  effect  on  the  degree  of  dissociation. 

Dissociation  of  Ammonium  Carbamate.  —  Carbamic  acid 


may  be  considered  as  carbonic  acid,  C^OH,  in  which  one 

X)H 
of  the  hydroxyl  groups  (OH)  has  been  replaced  by  the  amido 


group  (NH2),  C^-OH  .     The  ammonium  salt  is  formed  by 

\NH2 

the  direct  addition  of  NH3,  as  in  the  reaction  NH8  -f-  HC1 
=  NH4C1,  when  we  have  (NH3)2CO2. 
On  heating  ammonium  carbamate,  we  have 

(NH3)2C02  ^±  2  NH3  +  C02. 

Now  applying  the  mass  law,  we  have 


62  PHYSICAL   CHEMISTRY 

Since  the  carbamate  is  a  solid,  its  concentration  will  re- 
main practically  constant,  and  the  vapor  pressure  is  so  small 
in  comparison  to  the  pressures  of  the  dissociated  products 
that  it  can  be  neglected,  when  we  will  have 

Ki  =  C22  •  ct. 
Substituting  pressures  for  the  concentrations,  we  have 

K2    =  p2z  •  pz. 

But  the  total  pressure  is  the  sum  of  the  partial  pressures, 
i.e.  P  =  p2  +  ps,  and  since  there  are  twice  as  many  mole- 
cules of  NH3  as  of  CO2,  £2  =  2  p3.  Substituting  this  value 
for  pz  we  have 

P  =  2  p3  +  p3   or   />  =  3  p3   or   p3  =  £  P. 
Now  substituting  these  values  of  p%  and  p3  we  have 
^2=    (f  P)2-iP  or  K2  =  ^P^ 

It  is  evident  that  the  addition  of  ammonia  should  force 
back  the  dissociation  more  than  the  addition  of  carbon 
dioxide. 

In  the  case  of  ammonium  chloride,  NH4C1  ^±  NH3 
-f  HC1,  Neuberg  found  the  density  of  NH4C1  in  the  vapor 
form  to  be  1.13,  while  the  calculated  value  is  1.85.  In  an 
excess  of  34.6  cc.  of  HC1  the  density  was  1.5,  while  in  an 
excess  of  60  cc.  of  NH3  it  was  1.68.  The  dissociation  was 
forced  back  by  the  addition  of  either  of  the  components  of 
dissociation. 

Ammonium  hydrogen  sulphide  dissociates  according  to  the 
following  equation : 

NH4HS  ^±  NH3  +  H2S. 
(solid) 

Applying  the  mass  law  and  using  pressures,  we  have 
Kpi  =  p2  -  p3. 

But  since  NH4HS  is  solid,  the  concentration  of  NH4HS 
is  practically  constant,  and  its  vapor  pressure  is  so  small 


DEVIATIONS   FROM  THE   GAS  LAW  63 

that  it  can  be  left  out  of  consideration  without  introducing 
any  appreciable  error.  We  then  have  K2  =  p2  •  ps,  and 
since  P  =  p2  +  ps  and  the  number  of  dissociated  products, 
NH3  and  H2S,  are  equal,  p2  =  p3.  Substituting  p2  for  p3, 
we  have  P  =  2  p2  or  p2  =  -J  P.  Introducing  these  values  in 
the  original  equation  we  have  K2  =  (^  P)2. 


or 


=  |P*. 


Isambert   presents   the   following   experimental   data   in 
confirmation  of  the  dissociation  constant : 


VALUE  OF  _L_ 

TEMPERATURE 

4-P2 

Observed 

Calculated 

4.10°  C. 

37,900 

37,000 

7.00 

60,000 

58,OOO 

25.1 

62,500 

62,750 

At    25.1°,    P  =  501    mm.,    hence    £P2  =-^- =62,750, 

4 

when  the  products  of  dissociation  are  in  equal  molecular 
quantities. 

By  experiment  he  found  the  following  results,  when  the 
different  quantities  of  the  gases  were  present : 


61,152 
63,204 
60,882 
64,779 
62,504 


208 
138 
417 
452 


294 
450 
146 
146 


Mean 


This  is  a  close  agreement  with  the  theoretical  value  of 
approximately  62,750. 


CHAPTER  VII 
THE  PERIODIC   SYSTEM 

DALTON  presented  a  number  of  tables  illustrating  the 
"  relative  weight  of  the  ultimate  particles  of  gaseous  and 
other  bodies,"  but  it  was  not  until  1803  that  he  published 
his  first  table  of  atomic  weights,  and  this  was  not  printed 
until  1805.  This  table  was  on  the  basis  of  hydrogen  equal 
to  one.  The  other  table  of  atomic  weights  that  was  used 
during  the  early  part  of  the  last  century  was  that  of  Berze- 
lius,  which  was  on  the  basis  of  oxygen  equal  to  100.  With 
these  relative  weights  of  the  elements  available,  numerous 
efforts  were  made  to  find  relations  existing  between  the  ele- 
ments themselves  as  well  as  between  their  atomic  weights 
and  the  various  properties  of  the  elements. 

Prout's  Hypothesis.  —  Among  the  first  attempts  to  ex- 
press some  relationship  was  that  of  W.  Prout,  in  1815,  who 
aimed  to  show  that  the  atomic  weights  of  the  elements  were 
exact  multiples  of  that  of  hydrogen,  that  is,  that  the  ele- 
ments were  aggregates  of  the  fundamental  element  hydrogen. 
So,  if  the  atomic  weight  of  hydrogen  be  taken  as  unity, 
which  was  done  in  the  atomic  weight  table  of  Dalton,  the 
atomic  weights  of  the  other  elements  should  be  expressed  by 
whole  numbers.  This  hypothesis  of  Prout  had  many  sup- 
porters, among  whom  was  Thomas  Thomson,  who  accepted 
the  idea,  but  among  those  who  opposed  it  was  Berzelius,  who 
renounced  it.  In  the  efforts  to  substantiate  their  respective 
positions  a  vigorous  campaign  was  inaugurated,  which  re- 

64 


THE  PERIODIC   SYSTEM 


suited  in  the  early  establishment  of  accurate  values  for  the 
atomic  weights. 

It  was  found  that  the  value  given  by  Berzelius  for  carbon 
was  wrong,  and  Dumas  and  his  pupil  Stas  redetermined  it 
and  found  the  value  for  carbon  to  be  exactly  12.  This  fact 
aided  in  making  Dumas  a  strong  advocate  of  Prout 's  hy- 
pothesis and  also  led  to  the  extensive  accurate  atomic  weight 
determinations  of  Stas.  It  was  found  that  about  24  out 
of  the  70  elements  had  atomic  weights  that  did  not  vary 
from  a  whole  number  by  more  than  one  unit  in  the  first 
decimal  place.  (Of  the  elements  listed  in  the  Periodic 
Table,  page  72,  about  half  have  values  within  one  tenth  of 
an  integer.) 

In  Table  V  are  given  the  comparative  values  of  the  atomic 
weights  that  Prout  used,  and  the  values  for  191 5,  one  hun- 
dred years  later. 

TABLE  V—  (After  Harkins) 


, 

ATOMIC 

WEIGHTS 

ELEMENTS 

Prout  1815 

International 
i9i5(H=i) 

Hydrogen       ... 

I 

I  OO 

Carbon      

6 

1  1  01 

Nitrogen         

14 

IT.  qo 

Phosphorus         

14. 

?o  78 

Oxygen      

16 

IS  88 

Sulphur     
Calcium     • 
Sodium 

16 
20 

2J. 

31.82 
3976 

22  82 

Iron 

28 

e  c  JT 

Zinc 

•12 

64  86 

Chlorine 

^6 

•7C  46 

Potassium 

A.O 

18   80 

Barium 

7O 

1^6  ii 

Iodine 

I2d 

12^  Qd. 

The  values  used  by  Prout  were  the  best  available  at  that 
time,  but  the  result  of  the  accurate  work  of  Stas  and  others 


66  PHYSICAL  CHEMISTRY 

gave  values,  such  as  that  of  chlorine  (35.5),  which  were  hard 
to  reconcile,  and  Marignac,  who  favored  Prout's  hypothesis, 
suggested  that  a  unit  one  half  that  of  hydrogen  be  selected. 
Then  others  suggested  further  subdivisions  to  account  for 
the  other  irregularities,  with  the  result  that  this  brought 
Prout's  hypothesis  into  disfavor  for  a  time  at  least.  In 
1901  Strut t  concluded  from  the  theory  of  probabilities  that 
the  instances  of  the  atomic  weight  approximating  to  or 
being  a  whole  number  were  more  numerous  than  chance 
would  allow  and  hence  were  not  accidental,  but  indicated 
some  fundamental  fact  of  nature.  Prout's  assumption,  that 
all  elements  are  simply  condensations  of  hydrogen,  contains 
the  fundamental  idea  of  the  primal  element  or  "  mother 
substance  "  of  which  all  the  elements  are  composed  and 
has  been  variously  termed  "  earth,"  "  fire,"  "  protyle," 
hydrogen,  and  now  the  modern  scientists  embody  this  idea 
in  the  electron  theory.  That  this  idea  is  one  of  the  live 
questions,  as  it  was  one  hundred  years  ago,  is  evidenced  by 
the  extensive  investigations  at  present  along  this  line.1 

Doebereiner's  Triads.  —  Doebereiner  (1817)  arranged 
chemically  similar  elements  in  groups  of  three  in  the  order 
of  their  symbol  weights  and  showed  that  the  symbol  weight 
of  the  middle  one  was  the  mean  of  the  other  two.  There  is 
a  constant  difference  in  the  symbol  weights  of  succeeding 
members  of  the  triads  similar  to  the  difference  between 
homologous  series  in  organic  chemistry.  It  was  not  until 
1851,  when  Dumas  again  took  Up  this  idea  of  triads,  that  any 
interest  was  manifested ;  but  subsequent  to  this  time  many 
chemists  began  to  investigate  these  relations  between  the 

1  A  large  number  of  articles  have  recently  been  added  to  the  already 
extensive  literature.  Among  these  recent  contributions  reference  will 
be  given  to  a  few,  such  as  that  of  Sir  William  Ramsay,  Proc.  Roy.  Soc., 
A  92,  451  (1916) ;  Parson,  Smithsonian  Publication,  2371  (1915) ;  R.  A. 
Millikan's  recent  book,  The  Electron  (1917);  G.  N.  Lewis,  Jour.  Am. 
Chem.  Soc.,  35,  1448  (1914),  38,  762  (1916) ;  and  Harkins,  Ibid.,  39, 
856  (1917)- 


THE   PERIODIC  SYSTEM 


67 


properties  of  the  elements  and  the  relation  of  their  symbol 
weights. 

Table  VI,  in  which  are  given  some  of  the  more  important 
triads,  emphasizes  the  constant  differences  between  the  sym- 
bol weights. 

TABLE  VI 


ELEMENTS 

SYMBOL 
WEIGHTS 

DIFFERENCES 

MEAN  OF  EXTREME 
SYMBOL  WEIGHTS 

Lithium. 

6  Q4. 

•\f\  f\f\ 

Sodium         
Potassium         

Chlorine       
Bromine       
Iodine          

Sulphur        
Selenium      
Tellurium 

23.00 
39.10 

3546 
79.92 
126.92 

32.07 
79.2 
127  5 

16.10 

44.46 
47.00 

47-13 
48.3 

23.02 
81.19 
79.8 

Calcium 

40  o 

Strontium 

87  7 

47-7 

88.7 

Barium 

1-174 

49-7 

Phosphorus 

-JT    QA 

Arsenic 

74.  Q6 

43-92 

75.62 

Antimony                         .     . 

1  2O  2 

45-24 

In  the  following  series  of  triads  the  symbol  weights  are 
practically  the  same : 

Iron  .  .  •  55.85  Ruthenium  .  101.7  Osmium  .  190.9 
Cobalt  .  58.97  Rhodium  .  .  102.9  Iridium  .  .  193.3 
Nickel  .  58.68  Palladium  .  .  106.7  Platinum  .  195.2 

J.  P.  Cooke  (1854)  pointed  out  that  these  triads  did  not 
include  all  of  the  members  of  the  natural  groups  of  the  ele- 
ments, for  example,  fluorine  was  left  out  of  the  group  of  the 
closely  related  halogens.  This  idea  of  Cooke's  emphasized 
the  fallacy  of  trying  to  continue  this  method  of  grouping  the 
elements  into  triads. 


68 


PHYSICAL  CHEMISTRY 


THE  PERIODIC   SYSTEM  69 

Gladstone  (1853)  arranged  the  elements  in  the  order  of 
increasing  symbol  weights,  but  the  values  were  so  inaccurate 
that  no  relations  were  really  apparent.  Cannizzaro's  more 
accurate  values  enabled  Chancourtois  a  few  years  later 
(1862)  to  point  out  important  and  remarkable  relations 
between  the  physical  and  chemical  properties  and  the  sym- 
bol weights.  He  arranged  the  elements  in  a  spiral  around  a 
cylinder,  which  he  divided  into  16  vertical  sections.  The 
elements  in  any  vertical  section  were  found  to  have  analogous 
chemical  and  physical  properties.  This  arrangement  is 
known  as  the  Telluric  Screw. 

Newlands'  Law  of  Octaves.  —  Newlands  (1864-66)  ar- 
ranged the  elements  in  the  increasing  order  of  their  symbol 
weights  and  announced  his  Law  of  Octaves  as  follows :  "  If 
the  elements  are  arranged  in  the  order  of  their  equivalents 
with  a  few  slight  transpositions,  it  will  be  observed  that  ele- 
ments belonging  to  the  same  group  usually  appear  on  the 
same  horizontal  line ;  members  of  the  analogous  elements 
generally  differ  either  by  seven  or  some  multiple  of  seven. 
In  other  words,  members  of  the  same  group  stand  to  each 
other  in  the  same  relation  as  the  extremities  of  one  or  more 
octaves  in  music." 

The  Periodic  Law.  —  Mendele'eff  (1869)  and  Lother  Meyer 
(1869)  independently  and  practically  simultaneously  formu- 
lated periodic  systems  which  were  very  similar  to  that  put 
forth  by  Newlands,  but  they  were  not  familiar  with  it. 
Their  generalization,  commonly  known  as  the  Periodic  Law, 
is  expressed  by  the  statement  that  the  properties  of  the  ele- 
ments are  periodic  functions  of  their  symbol  weights. 

The  Atomic  Volume  Curve.  —  Meyer  paid  special  atten- 
tion to  the  physical  properties  and  expressed  the  symbol 
weights  as  periodic  functions  of  the  specific  gravities  of  the 
elements.  He  pointed  out  that  the  periodicity  is  more 
closely  manifest  in  the  so-called  atomic  volumes,  which  he 
defined  as  equal  to  the  symbol  weight  divided  by  the  specific 


70  PHYSICAL   CHEMISTRY 

symbol  weight 

gravity,  i.e.  -  ~- — =  atomic  volume.     He  plotted 

specific  gravity 

these  values  of  the  atomic  volumes  against  the  symbol 
weights  and  obtained  an  atomic  volume  curve  such  as  is 
represented  in  Fig.  5. 

The  whole  curve  is  made  up  of  a  series  of  periods  or 
waves.  The  summits  (i.e.  the  crests)  of  the  waves  are  oc- 
cupied by  the  alkali  metals : 

Cs  =  135,  Rb  =  85,  K  =  39,  Na  =  23,  and  Li  =  7 
Differences  47.5  46.5  16  16 

We  have  two  short  periods,  one  between  Li  and  Na  and  the 
other  between  Na  and  K.  Then  follow  two  long  periods, 
one  between  K  and  Rb  and  the  other  between  Rb  and  Cs. 
The  remainder  of  the  curve  is  partly  of  a  different  form  and 
is  evidently  incomplete,  and  there  is  no  reason  to  suspect 
another  alkali  of  higher  symbol  weight  than  Cs. 

By  a  consideration  of  the  troughs  of  the  curve,  differences 
between  the  long  and  short  periods  may  be  indicated.  The 
elements  of  minimum  atomic  volume  are  : 

Pt  =  191,     Rh  =  102,     Co  =  59,     Al  =  27,     B  =  n 
Differences  89  43  32  16 

These  differences  between  the  symbol  weights  of  the  ele- 
ments at  the  trough  of  the  curves  are  about  16  and  some 
multiple  of  16,  and  the  same  is  true  for  the  metals  that 
occupy  the  crests  or  peaks  of  the  curve.  The  elements  with 
the  smallest  atomic  volume  do  not  form  a  group,  as  do  those 
with  the  highest  atomic  volumes,  but  belong  to  two  widely 
different  groups,  which  do  not  show  any  chemical  analogy. 
Other  elements  fall  into  (i)  two  short  periods,  beginning  with 
Li  and  with  Na ;  (2)  two  complete  long  series,  beginning 
with  K  and  with  Rb ;  (3)  a  third  long  series,  beginning  with 
Cs  followed  regularly  by  Ba,  La,  and  Cr  and  interrupted  by 
the  intrusion  of  closely  related  rare  elements,  followed  again 
regularly  by  metals  from  Ta  to  Bi,  and  lastly  by  a  small 


THE   PERIODIC   SYSTEM  71 

portion  of  a  fourth  long  series.  We  thus  have  five  maximum 
and  six  minimum  sections  of  the  curve. 

The  descending  portion  of  the  curve,  representing  the  in- 
crease in  symbol  weight  and  decrease  in  atomic  volume,  is 
composed  of  the  so-called  base-f.orm.mg  elements.  The 
ascending  portions  are  occupied  by  the  acid-forming  elements, 
while  the  minima  portions  represent  the  elements  Al,  Mn, 
Ru,  Pd,  etc.,  which  are  not  decidedly  acid-forming  or  base- 
forming. 

The  position  of  elements  on  the  curve  is  closely  connected 
with  the  physical  as  well  as  the  chemical  properties.  Ele- 
ments chemically  similar  occupy  corresponding  positions  on 
similar  portions  of  the  curve.  At  the  maximum  positions 
we  find  the  light  elements ;  at  the  minimum  positions  the 
heavy  elements. 

The  Periodic  Table.  —  The  Periodic  Table  presented  by 
Mendel^eff  illustrates  the  periodicity  of  chemical  properties 
much  better  than  the  curve  that  we  have  just  been  consider- 
ing. The  following  modern  Periodic  Table  given  in  Table  VII 
is  practically  the  same  as  the  one  presented  by  Mendele'eff, 
except  that  the  symbol  weights  are  more  accurately  known 
and  the  new  group  of  the  rare  elements  in  Group  III  and 
Group  0  is  added. 

DISCUSSION    OF   THE    PERIODIC    TABLE 

Arrangement.  —  All  the  elements  are  arranged  in  suc- 
cession in  the  order  of  their  increasing  symbol  weights. 
Starting  with  Li  next  above  H,  we  find  that  the  one  above 
fluorine,  Na,  has  properties  very  similar  to  Li.  If  Na  be 
placed  in  the  same  vertical  column  with  Li  and  we  then 
arrange  the  other  elements  in  the  increasing  order  of  their 
atomic  weights,  the  elements  which  fall  in  the  same  vertical 
column  resemble  each  other  very  closely  chemically.  The 
set  of  seven  elements  starting  with  Li  agree  very  closely  with 
the  second  set  in  properties.  The  first  of  the  next  set,  K, 


72 


§ 


Offi 


offi 


PHYSICAL   CHEMISTRY 


o 


• 


-! 


55  * 


zs 


q 

(J  £ 


.«>  q 


I 

2 1 


s    • 
*!  o 


C  °0 

M     H 


s& 


•^  * 


M    ON 


•1 1 

a  8 

S  -d 

^  s 


HH      ^ 
6    SN 


.a.3 


eres 
ries 


11 


THE  PERIODIC  SYSTEM  73 

falls  into  the  group  with  Li  and  Na,  and  the  remainder  have 
a  striking  analogy  to  the  corresponding  element  of  the  other 
sets.  After  manganese  we  have  one  of  the  weakest  points 
in  the  Periodic  Law,  but  here  also  certain  regularities  are 
again  manifest  by  the  subsequent  elements. 

Chemical  Properties.  —  The  elements  on  the  left  are  ele- 
ments present  in  the  strongest  alkalies,  while  those  on  the 
extreme  right  are  the  elements  present  in  the  acids  and  are 
the  so-called  acid-forming  elements.  Between,  we  have  the 
gradation  between  acid  properties  and  basic  properties. 

Valency.  —  Valency  with  respect  to  oxygen  increases  from 
unity  for  elements  in  the  first  column  until  it  reaches  seven, 
when  the  valency  of  one  recurs  and  the  other  valencies  are 
repeated.  Valency  with  respect  to  H  decreases  from  left  to 
right. 

Periods.  —  The  first  14  elements  (not  counting  Group  0 
or  H)  arranged  in  the  horizontal  rows  constitute  what  is 
designated  two  short  periods,  for  the  eighth  of  these,  Na, 
has  chemical  properties  analogous  to  the  first  Li ;  the  ninth, 
Mg,  analogous  to  the  second,  Be,  the  tenth,  Al,  analogous 
to  the  third,  B,  and  so  on  to  the  seventh,  F,  which  has  chemi- 
cal properties  analogous  to  the  i4th  element,  Cl.  In  the 
next  elements  we  have  to  pass  over  14  before  we  find  one 
with  properties  similar  to  the  i4th,  K,  which  is  the  28th 
element,  Rb.  That  is,  we  have  passed  over  a  long  period, 
and  find  the  elements  arranged  in  a  long  period,  which  is 
followed  again  by  another  long  period  of  14  elements.  There 
are  two  short  periods  and  five  long  periods.  The  last  long 
periods  are  not  completely  filled  out,  and  there  are  a  number 
of  vacant  places.  When  the  Periodic  Tables  were  first  pre- 
pared many  of  the  elements  known  at  present  were  un- 
known, and  there  were  a  larger  number  of  vacant  places  in 
the  table  than  at  present.  Notable  among  these  were  the 
spaces  now  occupied  by  gallium,  scandium,  and  germanium. 
Mendeleeff  predicted  the  chemical  and  physical  properties 


74  PHYSICAL  CHEMISTRY 

that  the  elements  occupying  these  places  should  have.  A 
short  time  afterward  the  above-named  elements  were  dis- 
covered, and  they  were  found  to  have  the  properties  Mende- 
leeff  predicted  they  should  have.  This  fulfillment  of  proph- 
ecy brought  the  attention  of  the  scientific  world  to  Men- 
deleeff's  classification  and  resulted  in  the  rapid  adoption  of 
it.  It  was  soon  demonstrated  that  in  such  a  system  as  this 
we  had  not  only  a  means  of  prediction  but  also  the  only 
way  by  which  the  elements  could  be  grouped  together  as  a 
whole  for  the  purpose  of  representing  conveniently  and  con- 
cisely their  interrelations.  This  was  of  great  advantage. 
The  elements  in  the  atmosphere,  the  Argon  Group,  fall  into  a 
vertical  column  to  the  left  of  the  strongly  basic  elements, 
Group  I,  and  constitute  the  Zero  Group,  because  they  are 
inert  and  are  said  to  have  a  valency  of  zero. 

Physical  Properties.  —  There  are  many  other  physical 
properties  of  the  elements  and  of  their  compounds  which 
manifest  a  periodic  function  of  the  symbol  weights,  and 
among  these  may  be  listed  a  few  of  the  principal  ones. 

1 .  Malleability. 

(a)  Light  malleable  metals  occupy  the  points  of  maximum 
and  contiguous  portions  of  descending  curves ;    Li,  Be,  Na, 
Mg,  Al ;  K,  Ca ;  Rb,  Sr ;   Cs,  Ba. 

(b)  The  heavy  malleable  metals  are  found  in  the  lowest 
points  of  the  atomic  volume  curve  and  adjacent  sections  of 
the  ascending  curves ;    Fe,  Co,  Ni,  Cu,  Zn ;    Rb,  Pd,  Ag,  Cd, 
In,  Sn,  Pt,  Au,  Hg,  Tl,  Pb. 

(c)  Less  malleable  metals  are  found  just  before  the  lowest 
points  on  the  descending  curves ;    Ti,  V,  Cr,  Mn ;   Zr,  Nb, 
Mo,  Ru ;  Ta,  W,  Os,  Ir. 

(d)  Non-metallic  and  semi-metallic  elements  are  found  in 
each  section  on  the  ascending  branches  of  the  curves  preced- 
ing the  maximum. 

2.  Hardness  of  elements  is  inversely  proportional  to  their 
atomic  volume. 


THE  PERIODIC   SYSTEM  75 

3.  Melting  point  data  are   shown  diagrammatically  in 
Fig.  5  and  illustrate  the  periodic  function  of  this  property 
with  increasing  atomic  weight. 

(a)  All  gaseous  elements,  and  all  elements  that  fuse  below 
a  red  heat  are  found  on  the  ascending  portions  and  at  the 
maximum  points  of  the  atomic  volume  curve. 

(6)  All  infusible  and  difficultly  fusible  elements  occur  at 
the  points  of  the  minima  and  descending  portions  of  the 
curve.  The  periodicity  corresponds  to  that  shown  by 
atomic  volume  and  malleability.  For  those  elements  that 
are  easily  fusible  the  atomic  volume  is  larger  than  that  of 
the  element  with  next  smaller  symbol  weight.  There  are, 
however,  some  considerable  variations :  the  melting  point 
decreases  with  increase  in  symbol  weight  only  in  the  follow- 
ing :  (i)  Alkalies,  Li,  Na,  K,  Rb,  and  Cs,  (2)  Alkaline  earths, 
Mg,  Ca,  Sr,  Ba,  and  in  Cu,  Cd,  and  Hg.  The  compounds  of 
the  elements  also  exhibit  relations  in  their  melting  points. 
This  has  been  worked  out  by  Carnelley. 

4.  Volatility    is    intimately    associated    with    fusibility. 
Easily  fusible  volatile  metals  ar.e  found  on  the   ascending 
portions  of  the  atomic  volume  curve.     Elements  on  ascend- 
ing portions  of  the  curve  are  gaseous  and  easily  volatile,  but 
many  elements  of  high  atomic  weight  which  occupy  a  similar 
position,  however,  require  a  strong  red  heat  or  even  a  white 
heat  for  volatilization. 

5.  Fizeau  has  shown  that  the  volatile  elements  occurring 
on  the  ascending  curve  possess  almost  without  exception  a 
larger  coefficient  of  expansion  by  heat  between  o°  and  100° 
than  the  difficultly  fusible  elements  occupying  the  minimum. 
Carnelley  states  that  the  coefficient  of  expansion  of  an  ele- 
ment increases  as  the  melting  point  decreases. 

6.  The  refraction   of  light   by  the  elements   and   their 
compounds  is  also  essentially  related  to  the  symbol  weight. 

7.  Conductivity  for  heat  and  for  electricity  of  the  ele- 
ments are  dependent  upon  their  ductility  and  malleability, 


76  PHYSICAL   CHEMISTRY 

and  hence  are  periodic  functions  of  the  atomic  weights, 
the  periodicity  of  which  coincides  with  that  of  the  atomic 
volume. 

8.  Magnetic  and  dimagnetic  properties  of  the  elements 
appear  to  be  closely  connected  with  their  symbol  weights 
and  atomic  volumes.     Those  elements  the  atomic  volumes 
of  which  approach  the  minima  are  usually  magnetic.     Obser- 
vations differ  so  that  it  is  difficult  to  tell  whether  there  is 
a  periodic  relation  between  the  magnetic  and  dimagnetic 
properties  and  atomic  weights.     However,  from  maxima  to 
minima,  the  elements  are  entirely  magnetic,  and  at  minimum 
the  magnetism  exhibits  its  greatest  intensity.     This  is  true 
of  the  iron  group.     From  the  minimum  to  maximum,  follow 
dimagnetic  elements  only.     The  magnetic  susceptibility  is  a 
periodic  function  of  the  atomic  weight,  as  is  illustrated  in 
Fig.  5- 

9.  Electropotential  series  is  the  arrangement  of  elements 
according  to  electropositive  and  electronegative  character. 
These  properties  exhibit  variations  similar  to  those  exhibited 
in  malleability  and  brittleness. 

The  electrochemical  character  of  the  elements  becomes 
more  positive  as  the  symbol  weight  increases.  Cu  is  re- 
placed by  silver.  A  strongly  electronegative  element  Cl  will 
displace  a  weaker  one  I.  The  electropositive  character  be- 
comes less  marked  with  increase  of  symbol  weight  in  the 
groups  Cu,  Ag,  Au ;  Zn,  Cd,  Hg.  In  the  two  short  periods 
the  elements  become  regularly  less  electropositive  and  more 
electronegative  as  the  symbol  weight  increases,  but  in  the 
long  periods  the  change  is  less  regular.  The  elements  in  the 
groups  on  the  left-hand  side  of  the  table  are  electropositive 
and  those  on  the  right-hand  side  are  electronegative. 

Some  of  the  other  periodic  properties  are  the  following : 
The  crystalline  forms  of  various  compounds  of  the  elements, 
heats  of  chemical  combination,  ionic  mobilities,  distribution 
of  the  element  in  the  earth,  spectra  of  the  elements,  refrac- 


THE   PERIODIC   SYSTEM 


77 


tive  indices,  ultra-violet   vibration   frequencies,   solubility, 
electrode  potentials,  etc. 

Advantages  of  the  Periodic  Law  and  Classification.  — 
i .  It  affords  the  only  known  satisfactory  method  of  classify- 
ing the  elements  so  as  to  exhibit  the  relationship  of  the 
physical  and  chemical  properties  of  the  elements  and  of  their 
compounds. 

2 .  The  symbol  weights  of  the  elements  may  be  determined 
by  means   of   the  periodic   system   when   their  equivalent 
weights  are  known.     Many  of  the  symbol  weights  used  when 
Mendeleeff  presented  his  periodic  table  did  not  allow  plac- 
ing the  elements  in  the  position  which  corresponds  to  their 
properties,  so  he  assumed  that  there  had  been  an  error  made 
in  the  determination  of  the  equivalent  weight  or  that  the 
incorrect  multiple  had  been  selected.     For  example,  the  sym- 
bol weight  for  uranium  was  thought  to  be  60 ;    this  was 
changed  to  120,  and  finally  to  240  (238.5). 

3.  The  prediction  of  unknown  elements,  a  statement  of 
their  properties  and  general  chemical  characteristics.     As  an 
illustration,  in  the  following  table,  properties  of  the  proph- 
esied elements  are  compared  with  those  of  the  elements 
subsequently  discovered. 


PROPHESIED  ELEMENTS 


ELEMENTS  DISCOVERED 


Ek-aluminium 

Symbol  weight,  68 
Specific  gravity,  6.0 


Gallium 

Discovered  by  Lecoq  de  Bois- 

baudran  in  1875 
Symbol  weight,  69.5 
Specific  gravity,  5.96 


Eka-boron 

Symbol  weight,  44 
Oxide,  Eb2O3,  sp.  gr.  3.5 
Sulphate,  Eb2(SO4)3 
Double    sulphate    not    isomor- 
phous  with  alum 


Scandium 

Discovered  by  Nilson  in  1879 
Symbol  weight,  43.8 
Sc2O3,  sp.  gr.  3.86 
Sc2(SO4)3 

Sc2(SO4)3  •  3  K2SO4  -  slender 
prisms 


PHYSICAL   CHEMISTRY 


PROPHESIED  ELEMENTS 


ELEMENTS  DISCOVERED 


Eka-silicon 

Symbol  weight,  72 

Specific  gravity,  5.5 

Oxide,  EsO2,  sp.  gr.  4.7 

Chloride,  EsCLj,,  liquid,  boiling 
point  slightly  under  100°,  sp. 
gr.  1.9 

Ethide,  Es(C2H6)4,  liquid,  boil- 
ing point  160°,  sp.  gr.  0.96 

Fluoride,  EsF4,  not  gaseous 


Germanium 

Discovered  by  Winkler  in  1887 
Symbol  weight,  72 
Specific  gravity,  5.47 
Oxide,  GeO2,  sp.  gr.  4.7 
Chloride,   GeCU,   liquid,  boiling 

point  86°,  sp.  gr.  1.887 
Ethide,  Ge(C2H6)4,  liquid,  boiling 

point    1 60°,    sp.    gr.   slightly 

less  than  that  of  water. 
Fluoride,    GeF4  -   3  H2O,    white 

solid  mass 


Imperfections  of  the  Periodic  Law  and  Classification.  — 

We  have  seen  that  by  this  system  not  only  all  of  the  known 
elements  can  be  classified,  but  also  the  unknown  ones  as 
well.  It  is  not  surprising  then  that  from  such  a  universal 
proposition  there  should  be  some  variations  and  irregulari- 
ties, and  so  we  do  find  in  this  classification  a  few  weak  points. 
When  the  Periodic  Table  was  first  presented  there  was  a 
marked  discrepancy  in  the  arrangement  in  the  case  of  the 
following  elements,  but  according  to  the  present  accepted 
values  for  their  symbol  weights  that  has  disappeared,  as  is 
shown  in  Table  VIII. 

TABLE  VIII 


ELEMENT 

SYMBOL  WEIGHT, 
1870 

SYMBOL  WEIGHT, 
1916 

Osmium                       

108.6 

IQO.Q 

Iridium 

1  06  7 

iq^.l 

Platinum      

196.7 

195-2 

There  has  been  an  effort,  due  to  imperfect  knowledge  of 
the  law,  to  make  too  extensive  an  application,  or  to  limit  its 


THE  PERIODIC   SYSTEM  79 

sphere  of  activity,  and  hence  because  of  insufficient  and  in- 
accurate data  concerning  certain  elements  erroneous  con- 
clusions hare  been  drawn.  However,  there  still  remain  a 
few  remarkable  exceptions  to  the  Periodic  Law.  The  fol- 
lowing are  some  of  the  most  pronounced  ones : 

1.  In  Group  I  and  in  Group  VII,  the  elements  have  a 
valency  of  one,  and  since  the  valency  of  hydrogen  is  unity, 
it  could  be  placed  in  either.     Owing  to  the  fact  that  it  has  a 
low  boiling-point  and  that  its  formula  weight  is  represented 
(as  many  other  gaseous  elements)  as  diatomic,  H2,  it  is  in- 
cluded in  Group  VII  by  many  chemists.   Solid  hydrogen  does 
not  resemble  the  alkali  metals  in  physical  properties,  and  it 
is  typically  non-metallic.     Chemically,  however,  hydrogen 
acts  very  similarly  to  the  alkalies,  forming  stable  compounds 
with  non-metallic  elements,  such  as  the  halogens.      Owing 
to  this  it  is  placed  in  Group  I. 

2.  The  symbol  weight  of  argon,  39.88,  is  larger  than  that 
of  potassium,    39.15,   and   so   these   two   elements   should 
change  places.     With  argon  between  potassium  and  calcium 
we  should  have  a  decided  discontinuity  in  the  properties,  and 
furthermore,  this  would  bring  potassium  into  Group  0,  and 
the  properties  of  potassium  are  decidedly  unlike  those  of  the 
other  members  of  this  group. 

3 .  The  same  holds  for  tellurium  and  iodine  ;   they  should 
be  interchanged  according  to  their  symbol  weights,   but 
according  to  their  chemical  properties  iodine  must  be  placed 
in  Group  VII. 

4.  In  Group  VIII  we  have  iron,  cobalt,  and  nickel,  but 
from  the  symbol  weights  nickel  and  cobalt  should  exchange 
places.     Since  cobalt  and  iron  form  two  series  of  salts,  and 
nickel  forms  only  the  nickelous  salts,  the  gradual  variation 
in  the  properties  is  represented  by  placing  cobalt  between 
iron  and  nickel. 

5.  The  three  groups  of  triads  in  Group  VIII  are  peculiar 
in  that  the  triads  are  arranged  in  horizontal  lines  and  con- 


8o 


PHYSICAL  CHEMISTRY 


nect  the  members  of  the  three  long  series.  They  destroy 
somewhat  the  symmetry  of  the  whole  system. 

6.  Between  lanthanum,  139,  and  tantalum,  181,  there  are 
a  large  number  of  blank  spaces,  but  it  is  not  possible  to  fit  the 
fifteen  rare  earth  elements  into  these  places,  as  the  symmetry 
of  the  system  is  destroyed.  Since  these  elements  are  triva- 
lent,  they  are  grouped  together  in  Group  III. 

Graphic  Representations  of  the  Periodic  Table.  —  Many 
graphic  representations  of  the  periodic  arrangement  of  the 


FIG.  6.  —  Electro-Positive  Elements,  above  plane  of  paper,  black  letters  on  white 
ground.  Electro-Negative  Elements,  below  plane  of  paper,  white  letters  on 
black  ground.  Intermediate  Elements,  in  plane  of  paper,  black  letters  on 
sectioned  ground. 

elements  have  been  devised,  and  these  may  be  classified  as 
plane  diagrams  and  as  space  forms.  They  are  designed  to 
bring  out  more  distinctly  the  relation  of  the  properties  of  the 
elements  and  the  atomic  weights,  but  while  some  of  them 
well  express  the  relations  to  certain  properties,  others  do 
not,  but  represent  another  group  of  properties  better.  Many 
of  the  later  designs  of  the  space  forms  are  valuable  aids  in 
the  study  of  the  periodic  functions  of  the  atomic  weights. 


THE  PERIODIC  SYSTEM  8 1 

Only  one  of  the  best  of  these  will  be  presented  here  in  Fig.  6, 
which  is  the  space  form  according  to  Soddy,  wherein  the  figure 
8  design  is  employed.1 

1  For  other  graphic  designs  the  following  references  may  be  consulted, 
where  full  description  of  them  may  be  found  :  (i)  Crooks,  Chem.  News, 
78,  25  (1898),  employs  a  figure  8  form ;  (2)  Emerson,  Am.  Chem.  Jour., 
45,  1 60  (1911),  places  the  elements  on  a  helix;  (3)  Harkins  and  Hall, 
Jour.  Am.  Chem.  Soc.,  38,  169  (1916),  give  illustrations  of  a  number  of 
models,  many  of  which  are  their  own  designs. 


CHAPTER  VIII 
THE  KINETIC   THEORY   OF   GASES 

IN  our  preceding  considerations  we  found  it  desirable  to 
adopt  Avogadro's  Theory  of  the  structure  of  a  gas,  wherein 
it  is  assumed  that  a  gas  is  made  up  of  molecules  in  motion, 
which  in  turn  are  aggregates  of  one  or  more  atoms  which 
may  be  alike  or  of  different  kinds.  Bernoulli  published  in 
1738  the  fundamental  notions  of  the  Kinetic  Theory  of 
Gases,  in  which  he  pointed  out  that  the  pressure  of  a  gas  is 
due  to  the  impact  of  the  molecules  on  the  walls  of  the  con- 
taining vessel.  The  mathematical  theory,  however,  was 
developed  much  later  by  Clausius,  and  it  is  due  largely  to 
his  efforts  and  those  of  Maxwell  that  the  theory  as  now 
accepted  has  been  promulgated  and  developed. 

The  fundamental  assumptions  upon  which  the  Kinetic 
Theory  is  based  may  be  stated  as  follows  : 

1.  Gases  are  made  up  of  molecules  of  very  small  dimen- 
sions. 

2.  The  space  that  the  molecules  occupy  is  small  when 
compared  to  the  volume  of  the  gas  itself. 

3.  The  distance  of  the  molecules  apart  is  very  large  as 
compared  to  their  size,  i.e.  they  are  so  far  apart  that  they 
have  no  marked  influence  on  one  another. 

4.  The  molecules  are  in  rapid  motion  in  all  directions,  and 
are  assumed  to  be  perfectly  elastic. 

Deduction  of  The  Gas  Law  from  the  Kinetic  Theory  of 
Gases.  —  The  total  pressure  exerted  by  a  gas  on  the  walls 
of  the  containing  vessel  is  due  to  the  impacts  of  the  gas 

82 


THE  KINETIC  THEORY  OF   GASES  83 

molecules,  which  are  moving  in  all  directions,  against  the 
walls. 

Let  M  be  the  mass  of  a  given  gas  inclosed  in  a  box,  Fig.  7, 
whose  parallel  sides  are  all  rectangles,  the  inside  dimensions 
of  which  are  b,  c,  and  d.  If  m  rep- 
resents the  mass  of  one  molecule, 

M 

—  =  n,  the  number  of  molecules.    We 

m 

assume  that  these  n  molecules  of  the 
gas  are  moving  about  in  all  direc-  FIG 

tions.     Let  us  assume  that  there  is 

but  a  single  molecule  of  the  gas  in  the  box,  and  that  it 
is  moving  with  any  velocity.  The  force  that  this  molecule 
exerts  on  the  different  sides  is  found  as  follows :  The 
velocity  of  the  molecule,  u,  may  be  resolved  into  three 
components  perpendicular  to  the  faces  of  the  box.  Let  x 
represent  the  component  perpendicular  to  the  face  be ; 
y  represent  the  component  perpendicular  to  the  face  cd\ 
and  z  represent  the  component  perpendicular  to  the  face 
bd.  Then  the  force  exerted  by  the  face,  be,  upon  the 
molecule  may  be  found  by  the  formula  F  =  ma,  where 
F  represents  the  force,  m  the  mass  of  the  molecule,  and  a 
represents  the  acceleration  of  the  molecule  in  the  direction 

of  the  force.     But  acceleration  a  =  — — ,  where  v2  repre- 

t 

sents  the  velocity  after  impact  with  the  face,  and  vi,  the 
velocity  before  impact.  Substituting,  we  have  F  =  m^~v^ . 

The  molecule  strikes  the  face  be  with  the  velocity  x  normal 
to  the  face,  then  rebounds  from  the  face  with  a  velocity  —  x. 
That  is,  vi  =  x  and  vz  =  —  x.  The  effect  of  the  force  of 
impact  upon  one  face  is  distributed  over  the  period  of  time 
that  it  takes  the  molecule  to  travel  the  distance  2d,  when 

another  similar  impact  occurs.     This  time,  /,  is  equal  to  —  • 


84  PHYSICAL   CHEMISTRY 

Substituting  these  values,  for  vi,  v%,  and  /,  in  the  above  equa- 

„      m\  —  x—x]  mx2      TVT 

tion,  gives  r  =  — * — -, or — .     JNow,  since  the  torce 

2  d-  d 

X 

exerted  upon  the  face  by  the  molecule  is  equal  to  that 
exerted  by  the  molecule  upon  the  face,  but  in  opposite  direc- 
tion, we  may  write  the  force  exerted  by  one  molecule  upon 

the  face  be,  as  F  =  ^-.     The  force  exerted  by  the  molecule 

Ct  n 

2  Wt^C 

upon  the  two  parallel  faces,  be,  then,  is  — r~-  In  the  same 
way  the  force  exerted  by  the  molecule  upon  the  two  parallel 
faces  cd,  is  2  m^  ,  and  similarly  upon  the  two  faces  bd  is  2  mz 


b  c 

Let  us  assume  that  this  force  exerted  by  the  one  molecule 
is  the  mean  force  of  all  of  the  molecules ;  then  if  there  are  n 
molecules  the  total  force  or  pressure  upon  the  two  parallel 

faces  be  will  be  2  nmx  •     Similarly  on  the  two  parallel  faces 
d 

cd  the  pressure  will  be  2  nm/y  ,  and  on  the  two  parallel  faces 

I-,-,     M1i      2  nmz2 

bd,  it  will  be 

c 

If  we  designate  the  force  on  unit  area  by  p,  which  is  the 
intensity  of  pressure,  then  the  pressure  p  on  each  face  will 
be  the  same.  The  area  of  the  two  faces  be  is  2  be,  and  the 

total  force  is  2nm%  •  hence  the  pressure  p  will  be  x  • 

d  2  oca 

Similarly,  for  the  pressures  on  the  other  faces  we  have 

2 

2  cdb 

2  nmx' 


2bdc      P' 


THE   KINETIC  THEORY  OF  GASES  85 

• 
Adding  these  three  equations,  we  have 


: 

2  bed 

Simplifying  and  writing  the  mean  square  velocity  for  the 
sum  of  the  squares  of  the  three  components,  u2  =  #2  +  y2  +  z2, 


we  have  $p  =  ;   but  the  product,   bed,  of  the  three 

bed 

dimensions  of  the  box  is  the  volume,  hence,  substituting  V 
for  bed,  the  equation  becomes 


3  V 

Deduction  of  Boyle's  Law.  —  We  may  define  heat  as  the 
energy  due  to  the  position  or  velocity  of  the  molecules  of  a 
substance.  JHeat,  due  to  the  velocity  of  the  molecules,  we 
term  Thermal  Kinetic  Energy.  A  measure  of  this  Thermal 
Kinetic  Energy  is  Temperature,  then  T  =  f(muz)  . 

For  any  constant  temperature,  u  is  a  constant,  and  the 
mass,  nm,  of  the  gas,  is  also  constant  ;  therefore,  the  right- 
hand  member  of  the  equation,  J  nmu2,  is  a  constant.  The 
equation  may  then  be  written  pV  =  a  constant.  This  is 
Boyle's  Law,  which  we  have  deduced  from  the  Kinetic 
Theory  of  Gases. 

Deduction  of  Charles'  or  Gay  Lussac's  Law.  —  If  we  as- 
sume that  T  is  a  linear  function  of  mu2,  i.e.  T  =  k(mu?), 

then  substituting  in  pV  =  -  mnu2  we  get  pV  —  -  n—t  but 

3  3      £ 

-  T  is  a  constant,  hence  pV  =  T  X  a  constant  or  ^r=  0 
3/2  1 

constant.  Thus,  from  the  Kinetic  Theory  of  Gases  we  have 
derived  The  Gas  Law.  From  this  equation  we  also  have 
the  conclusion  that  at  constant  pressure  the  volume  of  a 
constant  mass  of  gas  is  directly  proportional  to  the  absolute 
temperature  ;  or,  if  the  volume  is  constant,  the  pressure  is 
directly  proportional  to  the  absolute  temperature,  i.e.  the 


86  PHYSICAL   CHEMISTRY 

coefficient  of  expansion  of  a  gas  is  a  constant,  which  is  Charles' 
Law. 

Deduction  of  Avogadro's  Hypothesis.  —  Let  us  now  apply 
the  equation  just  obtained  in  the  deduction  of  Boyle's  Law 
to  two  different  gases  which  are  under  the  same  conditions 
of  temperature  and  pressure  and  which  occupy  the  same 
volume.  This  equation  for  the  two  gases  becomes  re- 
spectively 

pV  =  J  miHiUj2  and  pV  =  \  m^n^u^ 

Hence  \  m\n\u?    =  J  m^n^-.  (i) 

It  has  been  shown  experimentally  that  when  two  gases  are 
under  the  same  conditions  of  temperature  and  pressure  they 
are  in  physical  equilibrium  and  may  be  mixed  without  change 
in  temperature.  We  conclude  from  this  that  the  kinetic 
energy  of  the  two  molecular  species  remains  unchanged,  and 
further,  that  at  the  same  temperature  the  kinetic  energy  of 
a  molecule  of  one  gas  must  be  equal  to  the  kinetic  energy 
of  a  molecule  of  any  other  gas.  Since  the  kinetic  energy  of 
a  molecule  is  ^  mu2,  then 

,  v 


Dividing  equation  (i)  by  equation  (2)  we  have  f  n\  —  f  HZ 


or 


That  is,  the  equal  volumes  of  all  gases  at  the  same  tem- 
perature and  pressure  contain  the  same  number  of  mole- 
cules. This  is  Avogadro's  Hypothesis. 

Molecular  Velocity.  —  Solving  equation  pV  =  J  nmu2  for 


u,  we  have  u*  =  or  u  =  V  or  «  =  .  (3) 

nm  w  nm  w  p 

This  equation  then  gives  us  the  velocity  of  the  molecules 
of  any  gas,  providing  we  know  its  volume  and  pressure  and 
the  quantity  of  gas  present. 


THE   KINETIC  THEORY  OF   GASES  87 

Let  us  calculate  the  velocity  of  the  hydrogen  molecule  at 
o°  Centigrade  when  under  one  atmosphere  pressure. 

m  X  n  =  mass  of  gas. 

One  gram-molecular  weight  of  a  gas  at  o°  and  i  atmosphere 
pressure  occupies  22.4  liters.  It  will  require  2.016  grams  of 
hydrogen  to  occupy  this  volume  under  the  conditions 
specified.  Hence,  substituting  these  values  in  the  above 
equation,  we  have 

^  /3  X  1033  X  980.6  X  22400 

u  —  \ 

2.OIO 

Solving  for  u  we  obtain  u  =  183,700  cm.  per  second,  or 
1.837  kilometers  per  second,  as  the  velocity  of  the  hydrogen 
molecule  under  the  conditions  of  our  problem. 

Diffusion  of  Gases.  —  The  molecules  of  a  gas  moving  in 
an  inclosed  space  bombard  the  walls.  Now,  if  there  is  an 
opening  in  one  side,  the  molecule  will  meet  with  no  resistance 
and  will  continue  in  its  path  on  through  the  opening  and 
thus  pass  out.  It  will  pass  through  with  the  original  speed 
it  possessed  inside  the  vessel,  and  this  speed  of  diffusion 
originated  directly  from  the  speed  of  the  molecular  motion, 
and  we  conclude  that  the  mean  speed  of  the  issuing  mole- 
cules must  therefore  be  proportional  to  the  mean  speed  of 
the  molecules  within  the  vessel.  Since  this  speed  is  propor- 
tional to  the  pressure  on  the  gas,  the  rate  of  outflow  will  be 
dependent  somewhat  on  the  resistance  the  gas  meets  in 
flowing  out.  If  the  gas  flows  through  a  very  small  aper- 
ture in  a  thin  membrane  into  a  vacuum,  then  the  resistance 
is  reduced  practically  to  the  minimum. 

If  we  have  two  gases  under  the  same  conditions  of  pres- 
sure and  temperature,  from  the  equation  u  =  \/—  we 

P 

have  ui'.uzi  :  Vp2 :  V/^.  That  is,  the  molecular  velocities  are 
inversely  proportional  to  the  square  roots  of  the  densities  of 
the  gases. 


88  PHYSICAL   CHEMISTRY 

This  relationship  may  be  deduced  not  only  from  the 
Kinetic  Theory  of  Gases,  but  it  has  also  been  developed  from 
flow  of  liquids  through  orifices,  which  fact  is  presented  as  an 
argument  in  favor  of  the  kinetic  theory.  Bernoulli  pre- 
sented a  theory  of  the  process  of  effusion  by  an  extension  to 
gases  of  Torricelli's  Law,  which  states  that  the  velocity  with 
which  a  liquid  issues  through  an  orifice  is  proportional  to 
the  square  root  of  the  pressure,  or  the  head  of  the  liquid. 

This  law  is  expressed  as  follows  :   v  =  \  —  ,  which  gives  us 

— 


the  same  relation  as  u  =  %-     deduced  from  the  Kinetic 

P 

Theory,  which  states  that  the  pressure  varies  as  the  square 
of  the  molecular  velocity. 

The  diffusion  of  gases  through  membranes  and  porous 
media  as  well  as  through  cracks  has  been  the  subject  of 
investigation  since  the  time  of  Priestley.  Graham  (1833) 
recognized  the  similarity  of  diffusion  and  the  passage  of  a 
gas  as  a  whole  through  fine  openings,  which  process  he 
termed  effusion  in  distinction  from  the  passage  of  a  gas 
through  capillary  tubes,  which  he  designated  transpiration. 
The  latter  process  did  not  conform  to  the  law  of  diffusion, 
while  the  process  of  effusion  did  conform  to  the  diffusion 
law.  Graham's  Effusion  Law  is  stated  as  follows  :  The  times 
required  for  equal  volumes  of  different  gases  to  flow  through 
an  aperture  is  proportional  to  the  square  roots  of  their 
densities.  This  law  is  true  for  the  flow  of  all  liquids  through 
a  small  orifice  and  was  employed  by  Bunsen  as  a  method 
for  the  determination  of  the  specific  gravity  of  gases.  It  has 
also  been  extended  to  the  determination  of  molecular  weights. 

If  ui  :  u*  :  :  Vp2  :  Vpi,  and  we  assume  the  same  volume  of 
the  two  gases  under  the  same  conditions  of  temperature  and 
pressure,  then  m\  :  m^  :  :  PI  :  P2,  since  the  molecular  weights 
are  in  the  same  ratios  as  the  densities  of  the  gases.  If  we 
refer  the  densities  to  that  of  some  standard,  such  as  air, 


THE   KINETIC  THEORY  OF   GASES 


89 


we  have  the  specific  gravities  Si  and  52.  Substituting,  we 
have  ui  :  Uz  :  :  Vs2  :  Vsi.  Since  the  times  of  efflux  of  equal 
volumes  are  inversely  proportionaljto  the  velocity  of  effu- 
sion, then  we  have  t\  :  t%  :  :  Vsi  :  Vs2.  That  is,  the  times  re- 
quired for  the  e  fusion  of  equal  volumes  of  different  gases  under 
the  same  conditions  of  temperature  and  pressure  are  directly 
proportional  to  the  square  roots  of  the  specific  gravities  of 
the  gases.  The  molecular  weights  are  proportional  to  the 
specific  gravities  ;  substituting,  we  have 


Table  IX  contains  some  of  Graham's  data  arranged  and 
recalculated  by  O.  E.  Meyer. 

TABLE  IX 


GAS 

SQUARE 
ROOT 

OF  THE 

SPECIFIC 
GRAVITY 

TIME  OF  EFFUSION  THROUGH  A 

Drawn  Out 
Glass  Tube 

Perforated   Brass  Plate 

I 

II 

Hydrogen 

0.263 

0-745 
0.984 

0.985 
0.986 
I.OOO 

1.051 

1.237 
1.237 

0.277 
0.756 
0.987 

0.276 

Marsh  gas 

0.753 

Carbon  monoxide      .... 
Ethylene 

0.987 

0.988 

Nitrogen      

0.984 
I.OOO 

1.053 
1.199 
1.218 

0.984 
I.OOO 

1.050 

Air     .     . 

Oxygen  

1.056 

Nitrous  oxide  
Carbonic  acid 

1.197 

1.209 

CHAPTER  IX 
SPECIFIC   HEAT   OF   GASES 

THE  amount  of  heat  required  to  raise  the  temperature  of 
a  substance  one  degree  is  known  as  the  heat  capacity  of  the 
body  and  will  be  designated  by  q.  If  the  amount  of  heat 
absorbed  by  a  body  when  its  temperature  is  raised  from  ti° 
to  AJ°  is  H  units  of  heat,  then  the  mean  heat  capacity  (qM) 

would  be  qM=-~1?- 

The  specific  heat  capacity,  C,  usually  called  the  specific 
heat,  of  a  substance  is  the  amount  of  heat  required  to  raise 
one  gram  of  the  substance  one  degree.  The  unit  of  heat, 
the  calorie,  is  defined  as  the  amount  of  heat  required  to 
raise  one  gram  of  water  one  degree  Centigrade.  The  amount 
of  heat  required  to  raise  the  temperature  of  one  gram  of 
water  one  degree  is  different  at  different  temperatures. 
Therefore  it  is  necessary  to  define  very  accurately  the  tem- 
perature used. 

Table  X  illustrates  the  variation  of  the  specific  heat  of 
water  with  the  temperature  as  given  by  Callendar  at  20°  C. 
as  the  unit. 

The  unit  employed  is  the  calorie  at  20°  C.,  while  the 
calorie  at  o°  would  be  1.0094  calories  at  20°,  and  the  mean 
calorie  between  o°-ioo°  is  equal  to  1.0016  calories  at  20° 
and  the  value  at  15°  is  equal  to  i.oon  calories  at  20°. 

The  atomic  heatoi  an  element  is  the  specific  heat  multiplied 
by  the  atomic  weight,  that  is,  C  times  atomic  weight  =  the 
atomic  heat.  Similarly,  the  molecular  heat  is  the  specific 
heat  of  the  substance  multiplied  by  the  molecular  weight. 

90 


SPECIFIC  HEAT  OF  GASES 
TABLE  X  —  SPECIFIC  HEAT  OF  WATER 


TEMPERATURE 

SPECIFIC  HEAT 

TEMPERATURE 

SPECIFIC  HEAT 

0 

.0094 

2O 

I.OOOO 

I 

.0085 

25 

0.9992 

2 

.0076 

30      . 

0.9987 

5 

.0054 

40 

0.9982 

10 

.0025 

50 

0.9987 

15 

.0011 

60 

I.OOOO 

16 

.OOO9 

80 

1.0033 

17 

.OOO7 

IOO 

1.0074 

If  a  gas  be  subjected  to  compression,  its  temperature  is 
raised  thereby.  On  heating  a  gas  the  amount  of  heat  re- 
quired to  raise  its  temperature  depends  upon  whether  this 
is  done  under  constant  pressure  or  constant  volume.  To 
keep  the  volume  of  a  gas  constant  when  it  is  heated,  an  in- 
crease in  pressure  is  required,  because  the  kinetic  energy  of 
rectilinear  motion  of  the  molecules  is  increased.  That  is, 
the  added  energy  is  changed  into  energy  of  motion  of  the 
molecules,  which  produce  additional  pressure.  If,  however, 
the  gas  is  allowed  to  expand  when  it  is  heated  and  the  pres- 
sure kept  constant,  work  must  be  done  to  move  this  external 
pressure  as  the  gas  expands.  In  the  latter  case  we  have 
what  is  designated  the  specific  heat  at  constant  pressure  Cp, 
and  in  the  first,  the  specific  heat  at  constant  volume  C9. 

The  difference  between  these  two  specific  heats  is  the  work 
done  against  the  external  pressure.  The  relation  between 
the  two  specific  heats  may  be  easily  determined. 

Let  us  assume  that  we  have  one  gram-molecule  of  gas 
under  standard  conditions  of  temperature  and  pressure,  and 
it  will  occupy  22.4  liters.  If  it  is  heated  from  o°  to  i°  C,  it 
expands  -g-fg-  of  its  original  volume,  or  2-7-3-  °f  22-4  liters 
=  0.08204  liter.  During  this  expansion,  work  is  done  in 
increasing  the  volume  against  the  pressure.  This  work  is 


PHYSICAL  CHEMISTRY 


equal  to  0.08204  liter  atmosphere.  But  0.08204  liter 
atmosphere  per  degree  is  the  constant  R  of  the  Gas  Law 
Equation.  Therefore  the  difference  between  the  molecular 
heat  at  constant  pressure,  mCp,  and  at  constant  volume, 
mCv,  is  R,  that  is,  mCp  =  mCv  +  R. 

R  may  be  calculated  in  calories  as  follows :  i  calorie  = 
42 ,690  gram-centimeters ;  R  expressed  in  gram-centimeters 
is 

1033.6X22400  =  84?8o  and  84780 
273  42690 

=  approximately  2  calories. 

The  molecular  heats,  mCv  and  mCp,  of  some  of  the  more 
common  gases  are  given  in  Table  XI. 


1.986    calories   or  R 


TABLE  XI 

The  values  for  mCp  were  determined  experimentally  and  mCv  by 
difference. 


GAS 

SPECIFIC  HEAT 
CP 

mCp 

mCv 

cP 

c* 

66 

Helium 

66 

^lercury 

2  Q6^ 

66 

Hydrogen   
Oxygen  . 

3-409 
O  2I7S 

6.880 
6  960 

4.880 
A   Q6O 

.412 
4.O 

Chlorine     
Hydrochloric  acid     .     .     . 
Nitrous  oxide  

O.I24I 
0.1876 

o  2262  . 

8.810 
6.85 
Q  QQ 

6.810 

4-85 

7  QQ 

.29 
.409 
I  24.7 

Methane     

0.893 

9-51 

7-51 

1.266 

The  heat  added  to  a  substance  may  be  utilized  in  (i)  in- 
creasing the  kinetic  energy  of  rectilinear  motion  of  the  mole- 
cules, manifesting  itself  only  in  a  rise  of  the  temperature ; 
(2)  in  performing  work  against  the  external  pressure  in  order 
to  expand  the  gas,  or  (3)  utilized  within  the  molecule  itself 
when  it  is  an  associated  or  polyatomic  molecule ;  and  (4)  in 


SPECIFIC  HEAT  OF   GASES  93 

overcoming  the  mutual  attraction  of  the  molecules.  In  the 
case  of  ideally  perfect  gases  the  molecules  are  out  of  the 
sphere  of  action  of  one  another,  and  consequently  the  effect 
of  this  last  consideration  is  very  small  and  therefore  prac- 
tically negligible. 

If  the  law  pV=RT  holds  for  the  gas,  the  specific  heat  of 
the  gas  must  be  independent  of  the  pressure  and  also  of  the 
volume.  The  whole  work  done  during  a  change  of  volume 
will  be  external.  If  the  volume  changes  from  Vi  to  v2  under 
constant  pressure  p,  the  external  work  will  be  p(v2  —  Vi). 
Now,  as  we  have  seen,  the  specific  heat  at  constant  pressure 
exceeds  that  at  constant  volume  by  the  thermal  equivalent 
of  the  work  required  to  overcome  the  resistance  offered  to 
the  expansion  of  the  gas. 

In  equation  mCp  —  mCv  =  R,  substituting  for  R  its  value, 

•2  —  ,  we  have 
273 

mCp  —  mCv  =  £  — 
273 

From  the  consideration  of  the  Kinetic  Theory  of  Gases 
we  found  that  pV  =  J  mnu2,  and  for  the  kinetic  energy 
K  =  %  (mn)u2. 

Equating  these,  we  have 


or  pV  =  %K, 

which  enables  us  to  express  the  molecular  energy  in  a  form 
which  can  be  readily  determined.  The  pressure  and  kinetic 
energy  of  a  gas  are  in  an  invariable  ratio  which  is  inde- 
pendent of  the  temperature.  Substituting  this  value  for  pV 
in  the  equation  above,  we  have 

mCp  -  mCv  =     2  K    • 
273X3 

All  of  the  energy,  E,  possessed  by  the  substance  is  the 
heat  required  to  warm  it  from  absolute  zero  to  the  given 


94  PHYSICAL   CHEMISTRY 

temperature  at  constant  volume.  This  is  increased  by  the 
heat  required  to  warm  the  gas  from  o°  to  i°,  that  is,  by 
•2^-5-  of  E.  But  this  heat  at  constant  volume  is  the  specific 

heat   at   constant   volume,    that   is,    mC9  =  —  ^—  E.     Then 

273 
dividing  the  above  equation  by  this,  we  have 

mCp  —  mCv 


In  case  the  total  energy  is  the  kinetic  energy,  then  K  =  E 
and  the  equation  becomes 


which  is  the  maximum  value  of  the  ratio  of  the  specific  heat 
at  constant  pressure  to  the  specific  heat  at  constant  volume. 
This  value  has  been  obtained  experimentally  in  the  case 
of  monatomic  gases,  mercury  vapor,  argon,  and  helium. 

In  the  case  of  diatomic  or  polyatomic  gases,  an  appreciable 
portion  of  the  heat  applied  to  raise  the  temperature  is  utilized 
in  overcoming  the  mutual  attraction  of  the  molecules  or  in 
intermolecular  work.  It  is  possible  to  raise  the  tempera- 
ture of  some  substances  to  such  an  extent  that  this  portion 
of  the  energy  increases  the  speed  of  the  atoms  within  the 
molecule  whereby  they  are  separated  from  their  combination 
with  the  others,  and  the  freed  atoms  thus  become  like  inde- 
pendent molecules,  the  atomic  energy  going  to  increase  the 
total  molecular  energy.  This  would  lead  us  to  the  conclu- 
sion that  the  kinetic  energy  of  the  atoms  would  be  decreased 
and  the  molecular  energy  increased,  hence  K  <  E.  It  is 
apparent  that  in  the  case  where  the  amplitude  of  vibration 
of  the  atoms  of  the  molecules  has  not  been  increased  suffi- 
ciently to  cause  them  to  pass  beyond  the  influence  of  the 
other  atoms  within  the  molecule,  just  before  dissociation 
takes  place,  that  we  will  have  the  maximum  of  heat  energy 


SPECIFIC  HEAT  OF   GASES  95 

being  utilized  in  the  atomic  energy.  The  more  atoms  there 
are  in  the  molecule,  the  greater  will  be  the  amount  used  in 
this  way  and  consequently  the  greater  the  decrease  in  the 
kinetic  energy  and  the  less  the  value  of  the  ratio : 

molecular  heat  at  constant  pressure  mCP  _ 
molecular  heat  at  constant  volume  mCv 

Hence  it  follows  that  by  determining  y  for  a  given  gas  or 
vapor,  it  would  be  possible  to  determine  the  complexity  of 
the  molecules. 

There  are  a  number  of  methods  by  which  the  value  of  y 
may  be  obtained,  and  it  is  not  always  necessary  actually  to 
determine  both  of  the  specific  heats. 

Laplace  showed  that  the  velocity  of  sound  in  a  gas  is 

expressed  as  follows  :  v  =  \— ,  where  v  is  the  velocity,  y  is 

1  P 

the  ratio  of  the  two  specific  heats,  p  the  pressure,  and  p  the 
density.  The  method  of  Kundt  and  Warburg,  which  is 
usually  employed,  is  a  means  of  finding  experimentally  the 
value  of  v.  The  apparatus  consists  of  a  "  Kundt 's  dust 
tube,"  and  as  employed  by  Ramsay  in  the  determination  of 
the  specific  heat  of  helium  consisted  of  a  long  tube  of  narrow 
bore,  closed  at  one  end,  through  which  is  sealed  a  glass  rod 
extending  for  an  equal  distance  inside  and  outside  of  the 
tube.  Some  lycopodium  powder  is  distributed  along  the 
tube  and  dry  air  is  introduced.  The  glass  rod  is  set  in  vibra- 
tion by  rubbing  it  with  a  cloth  wet  with  alcohol.  By  mov- 
ing the  clamp  on  the  rubber  tubing  which  closes  the  other 
end  of  the  tube,  the  length  can  be  adjusted  till  it  resounds 
to  the  proper  note.  The  interference  of  the  waves  deposits 
the  lycopodium  in  piles  at  the  nodes.  The  distance  be- 
tween these  nodes  represents  one  half  the  wave  length  and 
can  be  readily  measured.  Air  is  then  removed  by  evacua- 
tion, and  the  tube  is  refilled  with  the  gas  under  investiga- 
tion and  the  wave  length  determined. 


96  PHYSICAL  CHEMISTRY 

Let  X  represent  the  wave  length  of  a  sound  of  frequency  n 
in  any  specified  gas  ;  let  p  =  the  pressure  and  p  its  density, 
then  from  Laplace's  formula  we  have  for  any  two  gases 
under  the  same  pressure  and  temperature  : 


and    % 
*  pi  pz        vz         pi  yz 

Since    the    densities    are    proportional    to  the  molecular 
weights,  we  may  write  the  equation 


yz  mi 
which  becomes 


Vz       yz  mi 

Taking  air  as  the  standard  gas,  y\  =  1.408  ;  the  value  of  y 
for  any  other  gas  is  then  obtained  by  comparing  the  wave 
lengths  of  the  same  sound  in  the  gas  and  in  air,  providing 
the  molecular  weight  or  density  of  the  gas  is  known.  The 
velocity  is  equal  to  the  wave  length  times  the  number  of 
vibrations  (pitch)  in  a  unit  of  time.  If  x  is  the  distance 
between  the  nodes  or  ridges  of  dust,  then  X  =  2  x  and  the 
velocity  is  2  nx.  Then  we  would  have  vi  =  2  nx\,  and  vz 
=  2  nxzj  which,  substituted  in  the  above  equation,  gives 


Substituting  the  value  for  air,  y\  =  1.408  and  m\  =  28.9, 
the  value  for  y2  can  be  obtained  if  the  other  values  are 
known  ;  xz  and  x\  being  obtained  experimentally  and  mz 
being  known. 


CHAPTER  X 
VAN  DER  WAALS'   EQUATION 

WE  saw  that  the  Laws  of  Boyle,  Gay  Lussac,  and  Avo- 
gadro  are  only  strictly  applicable  to  perfect  gases.  Under 
low  pressure  the  deviation  is  small,  but  it  is  greater  when 
gases  are  highly  compressed.  We  considered  that  the  ki- 
netic energy  of  rectilinear  motion  of  the  molecules  is  directly 
proportional  to  the  absolute  temperature  under  all  condi- 
tions, and  so  certain  modifications  in  the  Kinetic  Theory 
were  suggested  by  van  der  Waals  to  explain  the  observed 
variations. 

In  the  Kinetic  Theory  the  pressure  due  to  the  bombard- 
ment of  the  walls  of  the  vessel  by  the  molecules  of  the  gas  is 
calculated  on  the  assumption  (i)  that  the  actual  volume 
occupied  by  the  molecules  is  inappreciable  compared  with 
the  total  volume  of  the  gas,  and  (2)  that  the  molecules  exert 
no  appreciable  attraction  for  each  other.  It  is  found  that 
when  the  gas  is  greatly  rarefied,  this  assumption  is  admissible, 
but  when  the  molecules  are  brought  close  together  by  com- 
pression of  the  gas,  it  is  not ;  hence  the  Gas  Law  Equa- 
tion must  be  modified  to  take  these  facts  into  consideration. 
Many  attempts  have  been  made  to  correct  the  Gas  Law 
Equation  for  this  purpose,  the  most  successful  being  that 
of  van  der  Waals  (1879). 

According  to  the  Kinetic  Theory  the  total  volume  occupied 
by  the  molecules  is  small  in  comparison  to  the  total  volume 
of  the  gas.  Van  der  Waals  corrected  for  the  volume  actually 
occupied  by  the  molecules  thus  : 

97 


98  PHYSICAL   CHEMISTRY 

Let  b  =  volume  occupied  by  molecules  of  gas 
v  =  volume  of  the  gas 

then  (v  —  6)  =  the  actual  or  free  space  in  which  the  mole- 
cules are  free  to  move,  and  when  the  gas  is  subjected  to 
pressure  this  is  the  part  which  decreases  in  volume. 

In  1854  Joule  and  Thomson  showed  experimentally  that 
strongly  compressed  gases  are  cooled  by  expansion.  Then, 
on  expansion,  work  is  done  against  the  molecular  force,  and 
we  conclude  that  the  molecules  have  attracted  one  another. 
Hence  a  certain  cohesion  is  ascribed  to  the  gases,  which  is 
more  noticeable  the  greater  their  density.  Under  high  pres- 
sure gases  contract  more  than  they  should  according  to 
Boyle's  Law,  and  this  is  explained  on  the  supposition  that 
in  compression  the  molecules  are  drawn  more  closely  together 
by  their  attractive  force,  and  this  tends  to  aid  the  external 
pressure  in  making  the  volume  smaller.  Therefore  this 
factor  should  be  added  to  the  external  pressure.  This  force 
must  be  proportional  to  the  number  of  molecules  attract- 
ing each  other,  that  is,  to  the  density  of  the  gas,  since  the 
density  of  a  given  gas  is  proportional  to  the  number  of 
molecules  per  unit  volume.  Van  der  Waals  concluded  that 
the  attraction  is  proportional  to  the  square  of  the  density 

or  inversely  to  the  square  of  the  volume,  and  gave  -^-  as  the 

expression  for  this  correction. 

Substituting  these  two  values  in  the  Gas  Law  Equation  we 
have 

+  -rk\(V-b)-RT 


•which  is  known  as  van  der  Waals'  Equation  of  Condition. 
This  equation  gives  the  behavior  of  the  so-called  permanent 
gases,  of  the  easily  condensed  gases,  and  it  is  also  claimed 
that  it  can  be  applied  to  the  liquid  state  as  well,  although 
Tait  has  pointed  out  that  it  does  not  hold  for  any  real  liquid. 


VAN  DER  WAALS'   EQUATION 


99 


It  is  apparent  that  when  the  volume  is  large,  the  correct- 
ing factors,  —  and  b,  have  no  appreciable  influence  and  the 

equation  is  really  pV  =  RT.    When  the  pressure  is  very 
great,  the  factor  b  ceases  to  be  negligible,  and  its  influence 

increases  more  rapidly  than  -^  •     The  product  p  V  reaches  a 

minimum,  and  afterwards  increases,  and  eventually  becomes 
much  greater  than  at  low  pressures. 

For  ethylene,  which  is  readily  liquefiable,  Baynes  calcu- 
lated the  values  of  p  V  from  the  following  formula  : 

(  V  -  0.0024)  =  0.0037  (272.5  +  0 

where  pV  =  1000  for  p  =  i  atmosphere  at  20°  C.     The 
observed  values  in  Table  XII  are  from  Amagat's  results. 


TABLE  XII 


p 

pv 

Observed 

Calculated 

I 

IOOO 

IOOO 

31.6 

914 

895 

72.9 

416 

387 

110.5 

454 

456 

176.0 

643 

642 

282.2 

941 

940 

398.7 

1248 

1254 

Van  der  Waals  assumed  that  the  molecules  of  an  ordinary 
substance  undergo  no  alteration  during  the  process  of 
liquefaction,  and  his  equation  is  intended  to  apply  only  to 
such  substances.  When  association  takes  place,  the  rela- 
tion between  pressure,  volume,  and  temperature  becomes 
complex. 


100  PHYSICAL  CHEMISTRY 

If  V  remains  constant,  then 


takes  the  form 

(p  +  QC  =  RT 


R 
where  C  and  Cf  are  constants  and  k  =  ^  • 

That  is,  the  p  is  a  linear  function  of  the  absolute  tempera- 
ture when  the  volume  of  the  mass  remains  constant. 

The  constants  a  and  b  in  van  der  Waals'  equation  may  be 
calculated  from  experimental  data  ;  or  from  a  number  of  iso- 
therms the  pressure  and  temperature  at  a  series  of  constant 
volumes  may  be  read  off  and  the  values  of  the  constants  k 
and  C  in  the  formula  p  =  kT  —  C  calculated  for  each  volume. 

Clausius  (1880)  claimed  that  van  der  Waals'  equation  did 
not  represent  the  facts  with  sufficient  exactness  and  de- 
veloped an  equation  himself  which  allowed  for  the  variation 
of  molecular  attraction  with  change  in  temperature. 

RO  r 

The  Clausius  equation,  p  =  —  --  —  -  -  —  ,  contains 

V  —  a      B(v  -\-  B) 

four  constants,  R,  c,  a,  B,  which  necessitate  four  experiments 
on  p  and  V  at  different  temperatures  to  establish,  and  it  is 
claimed  to  give  greater  range  and  better  agreement  than 
van  der  Waals'  equation  which  contains  only  three  con- 
stants. 

APPLICATION  OF  VAN  DER  WAALS'  EQUATION 

The  following  quotation  is  Andrews'  description  (1863) 
of  his  experiments  on  the  behavior  of  carbon  dioxide 
when  subjected  to  changes  of  pressure  and  of  temperature  : 
"  On  partially  liquefying  carbonic  acid  by  pressure  alone  and 
gradually  raising  at  the  same  time  the  temperature  to  88°  F. 


VAN   DER   WAALS;   EQ(JATIQ$)  '„-•'',  ;^  \\  \  \  SOI 


the  surface  of  demarcation  between  the  liquid  and  gas 
became  fainter,  lost  its  curvature,  and  at  last  disappeared. 
The  space  was  then  occupied  by  a  homogeneous  fluid,  which 
exhibited,  when  the  pressure  was  suddenly  diminished  or 
the  temperature  slightly  lowered,  a  peculiar  appearance  of 
moving  or  flickering  striae  throughout  its  entire  mass.  At 
temperatures  above  88°  F.  no  apparent  liquefaction  of  car- 
bonic acid,  or  separation  into  two  distinct  forms  of  matter, 
could  be  effected  even  when  a  pressure  of  300  or  400  atmos- 
pheres was  applied.  Nitrous  oxide  gave  analogous  results. " 

Andrews  plotted  the  results  of  his  experiments,  and  the 
curves  in  Fig.  8  represent  them. 

The  p-V  curve  of  constant  temperature,  isothermal  curve, 
for  gases  that  obey  Boyle's  Law,  should  be  a  rectangular 
hyperbola,  and  the  curve  for  CC>2  at 
48.1°  approximates  this  closely.  At 
35.5°  the  curve  has  a  decided  flexure, 
while  at  32.5°  this  is  more  marked, 
and  at  31.1°  still  more  marked,  when 
we  have  a  double  flexure.  This 
curve  runs  for  a  short  distance  paral- 
lel to  the  F-axis  and  represents  the 
critical  temperature  of  CO2.  The 
volume  diminishes  regularly  with  in- 
crease in  pressure  at  this  tempera- 
ture until  a  pressure  of  73  atmos- 
pheres is  reached,  when  the  volume 
decreases  very  rapidly,  about  one 

half  of  it  disappearing.  A  steady  increase  in  pressure  is 
required  to  produce  this  change,  and  by  the  time  77 
atmospheres  are  reached  we  have  a  homogeneous  mass 
which  responds  to  a  regular  change  in  volume  with  in- 
creased pressure.  At  21.5°  we  have  the  volume  gradually 
decreasing  with  increased  pressure  until  about  60  atmospheres 
are  reached,  when  there  is  a  sudden  break  in  the  curve  which 


FIG.  8. 


CHEMISTRY 

runs  parallel  to  the  V  axis,  showing  a  marked  decrease  in 
volume  without  change  in  temperature.  This  is  similar  to 
the  curve  at  13.1°,  which  becomes  horizontal  at  49  atmos- 
pheres pressure,  showing  a  change  of  about  f  the  volume  a 
perfect  gas  should  occupy  at  this  temperature. 

Andrews  from  his  experimental  work  insisted  on  the  idea 
of  the  continuous  passage  of  vapor  into  the  liquid  form  on 
increasing  the  pressure,  and  Thomson,  in  an  effort  to  explain 
the  shape  of  the  isotherms  just  above  the  critical  tempera- 
ture, prescribed  an  hypothesis  in  confirmation  of  this  idea 
as  illustrated  by  Fig.  8. 

FGH  represents  the  isotherm  above  the  critical  tempera- 
ture and  pressure,  where  van  der  Waals'  equation  assumes  a 
continuous  passage  from  the  liquid  to  the  vapor  state  or 
vice  versa.  The  line  ABC,  which  is  a  broken  line,  repre- 
sents the  ordinary  isotherm  of  a  substance  passing  from  the 
liquid  to  the  gaseous  state.  The  part  A  B  refers  to  the 
liquid  state,  at  B  the  vapor  pressure  is  equal  to  the  external 
pressure,  and  the  substance  begins  to  separate  into  saturated 
vapor  and  liquid.  The  horizontal  portion  BC  shows  that 
while  this  change  is  taking  place  the  pressure  remains  con- 
stant and  represents  the  isotherm  of  the  mixture.  The  por- 
tion CD  represents  non-saturated  vapor,  and  the  isotherm 
approximates  more  nearly  that  of  a  perfect  gas. 

James  Thomson  suggested  that  A  A'  and  CD  are  portions 
of  the  same  continuous  curve  and  are  connected  by  some 
ideal  branch,  such  as  AMBNC,  along  which  the  substance 
might  pass  continuously  from  liquid  to  gaseous  condition 
below  the  critical  temperature,  as  it  does  above  that  tem- 
perature, without  separation  into  two  distinct  states  simul- 
taneously existing  in  contact  with  each  other.  Along  AM 
we  have  the  condition  of  superheated  liquids,  and  along  C N, 
supersaturated  vapors.  So  the  abnormal  conditions  of  both 
liquid  and  vapor  are  represented  by  Thomson's  curve 
AMB  NC,  as  conditions  of  unstable  equilibrium.  The  vapor 


VAN  DER  WAALS'  EQUATION  103 

at  A7  is  supersaturated,  it  condenses  when  equilibrium  is 
destroyed,  and  if  the  temperature  be  kept  constant,  a  de- 
crease of  pressure  to  the  point  n  will  take  place.  Similarly 
at  M  we  have  a  superheated  liquid  which  on  disturbing  the 
equilibrium  assumes  a  condition  of  stable  equilibrium  with 
explosive  violence  and  assumes  the  condition  represented  by 
m  when  the  substance  is  partly  liquid  and  partly  vapor. 
Between  N  and  M  we  have  the  volume  and  pressure  in- 
creasing simultaneously,  a  condition  difficult  to  realize  in  a 
homogeneous  mass.  It  is  apparent  that  the  pressure  curve 
cuts  the  Thomson  hypothetical  curve  at  three  points,  A,  B, 
and  C,  which  would  correspond  to  three  different  values  for 
the  volume  for  the  one  value  of  the  pressure.  As  the  pres- 
sure increases  it  is  apparent  that  the  Thomson  curve  de- 
creases in  length,  the  difference  between  the  three  values  of 
the  volumes  becomes  less ;  and  as  we  approach  the  critical 
point  these  values  likewise  approach  this  value  of  the  critical 
volume  as  their  simultaneous  and  limiting  value. 

Realization  of  Parts  of  Curve  Experimentally.  —  i.  Methyl 
formate  (31.9°  B.  Pt.)  was  heated  to  80°  and  the  whole  of 
the  vapor  condensed.  Pressure  was  lowered  below  800  mm. 
without  boiling  taking  place ;  at  80°  the  vapor  pressure  is 
3500  mm.,  so  that  the  pressure  was  reduced  to  less  than  one 
fourth  of  the  vapor  pressure ;  in  other  words,  it  was  more 
than  45°  above  its  boiling  point  under  800  mm.  and  80°  C. 
Boiling  finally  took  place  with  explosive  violence. 

2.  Worthington  showed  that  when  a  sealed  tube,  nearly 
full  of  pure  liquid  free  from  air,  is  gently  warmed  until  the 
liquid  fills  the  tube  completely,  a  bubble  of  vapor  will  not 
form  on  cooling  until  a  very  large  negative  pressure  is  reached. 
The  tubes  collapsed  in  some  cases. 

3.  Aitken  showed  that  temperature  of  dust-free  vapors 
could  be  lowered  many  degrees  below  the  condensing  point 
before  liquefaction  takes  place. 

It  is  therefore  proved  that  part  of  the  continuous  isother- 


104  PHYSICAL   CHEMISTRY 

mal  (Fig.  8)  from  A  to  M  and  from  C  towards  N  may 
be  realized  experimentally.  From  M  to  N  increase  in  vol- 
ume is  attended  with  rise  of  pressure,  and  if  it  could  be 
brought  about,  would  take  place  with  explosive  rapidity. 

CALCULATION    OF    CRITICAL    CONSTANTS    FROM    VAN    DER 
WAALS'.  EQUATION 

The  Gas  Law  Equation  pV  =  RT,  when  corrected  for 
the  volume  b,  actually  occupied  by  the  molecules  and  the 

mutual  attraction  of  the  molecules,  -^,  gives  us  van  der 
Waals'  equation  : 

(i) 


which,   when  rearranged  in   the  order  of  the  decreasing 
powers  of  V,  gives 


p  J         p        p 

Under   normal   conditions   of   temperature,    when    V  =  i, 
p  =  i,  and  T  =  273,  equation  (i)  becomes 

(i  +  a)  (i  -  6)  =  273  R  (3) 

Solving  for  R,  we  have 

R  _  d  +  a)  d  -  b) 

273 
Substituting  this  value  of  R  in  equation  (2),  we  have 


2  +  av_a   =  Q  (  } 

273  £  p         p 

This  is  a  cubic  equation  with  respect  to  V,  if  p  is  con- 
stant, with  three  roots,  one  or  all  of  which  may  be  real.  We 
saw  that  there  is  one  temperature  at  which  the  three  values 
of  V  for  one  value  of  p  become  equal  and  that  is  at  the  Crit- 
ical Temperature.  But  at  this  temperature  the  pressure  is 


VAN  DER  WAALS'   EQUATION  105 

designated  the  critical  pressure  and  the  volume  the  critical 
volume.  Let  us  designate  these  critical  values  for  V,  p, 
and  T  respectively  as  follows  :  Ve,  pn  and  Te.  If  the  three 
roots  are  equal,  they  become  the  critical  volume  Ve,  and  the 
cubic  equation  becomes  (  V  —  Ve)3  =  o,  which,  on  expanding, 
becomes 


which  is  equivalent  to  our  equation  (4). 

Equating  1  the  coefficients  of  equations  (4)  and  (5),  where 
Vc  is  the  critical  volume,  and  remembering  that  the  corre- 
sponding values  for  T  and  p  are  their  critical  values,  we 
then  have 

3V.  =  b  +  (l+a)^-b)Tt  (6) 

273ft 

3^2  =  (7) 


From  these  three  equations  we  can  calculate  the  critical 
values  in  terms  of  a  and  b,  the  constants  of  van  der  Waals* 
equation. 

Dividing  (8)  by  (7),  we  have 


3V.1     P.     <* 

^=b 

3 

1  Wells  states  the  Theorem  of  "[Indeterminate  Coefficients  as  follows  : 
If  the  series  A  +  Bx  +  Cxz  +  Dx*+  ...  is  always  equal  to  the  series 
A  '  +  B  'x  +  C'x2  +  D  'x3  +  .  .  .  where  x  has  any  value  which  makes 
both  series  convergent,  the  coefficients  of  like  powers  of  x  in  the  two 
series  will  be  equal;  that  is,  A  =  A',  B  =  B',  C  =  C',  D  =  D',  etc. 
From  this  we  have  the  following  rule  :  If  two  equations  represent  the 
same  locus  and  one  term  of  one  equation  is  exactly  the  same  as  one 
term  of  the  other,  then  the  coefficients  of  like  powers  of  the  variable  are 
equal. 


106  PHYSICAL   CHEMISTRY 

Then  Ve  =  3  b  (critical  volume).  (9) 

Substituting  this  value  in  (7),  we  have 


Solving  for  pe 


pe  =  —       (critical  pressure).  (10) 

Substituting  these  values  of  Ve  and  pe  in  equation  (6)  we 
have 


If  we  desire  to  retain  the  value  of  the  gas  constant  R  in 
the  equation,  instead  of  expressing  the  initial  standard  con- 

ditions as  P°    °  and  defining  them  as  po  =  i  ,  V0  =  i  ,  and 
TO 

To  =  273,  we  could  have  kept  this  as  R,  and  equation  (4) 
would  take  the  form 

RI]V*+aV-ri=0  (12) 

P  )          P          P 

and  equation  (6)  would  become 

3  f.  =    &+££  (13) 


From  which  Te  can  be  calculated  by  substituting  values 
of  Vc  and  pc  from  equations  (9)  and  (10)  respectively,  and 
we  have 


VAN  DER  WAALS'  EQUATION  107 

RTe 


27 


a 
8  a 


Conversely,  we  may  express  the  values  of  the  constants 
a,  b,  and  /?  in  terms  of  the  critical  values. 
From  equation  (9), 


Solving  for  6,  we  have 

b  =-7  (i5) 

o 

From  equation  (10), 

*---^ 

27  62 

Solving  for  a,  we  have 

a  =  27  62£c  (16) 

Substituting  the  value  of  b  from  (15),  we  have 

'-^t'-sV-'P-  (,7) 


Solving  equation  (14)  for  R,  we  have 


and  substituting  the  value  of  a  from  (17)  and  b  from  (15), 
we  have 

R  -  8  •  3  Vfp. 


108  PHYSICAL   CHEMISTRY 

which  simplifies  to 


THE  REDUCED  EQUATION  OF  STATE 

If  we  substitute  in  van  der  Waals'  equation  the  values  of 
critical  values  of  the  pressure,  volume,  and  temperature,  we 
have 


This  may  be  simplified  if  we  divide  each  side  of  the  equa- 


tion  by    -^-*"  ;  dividing  the  first  factor  of  the  left  member 

O 

by  pe  and  the  second  by  — e- ,  we  have 

O 

«X-  (22) 


It  is  apparent  that  the  values  of  the  pressure,  volume,  and 
temperature  are  expressed  as  factors  of  the  critical  values, 
hence  if  we  substitute  for  these  fractions 


we  have 

(3  *  ~  i)  =  8  6. 


Therefore,  expressing  V,  p,  and  T  respectively  in  frac- 
tions of  the  critical  volume,  pressure,  and  temperature,  the 
equation  of  condition  assumes  the  same  form  for  all  sub- 
stances, or  if  two  liquids  be  taken  under  the  conditions  of 
temperature  and  pressure  which  are  the  same  fractions  of 


VAN  DER  WAALS'  EQUATION 


109 


their  respective  critical  values,  such  conditions  are  known 
as  corresponding  conditions;  the  law  is  called  the  Law  of 
Corresponding  States,  and  the  equation  is  the  Reduced  Equa- 
tion of  State.  • 

This  equation  is  independent  of  the  substance  and  of  the 
physical  state  of  the  substance,  as  there  are  no  arbitrary 
constants,  provided  that  molecular  association  or  dissocia- 
tion does  not  take  place.  Young  investigated  this  relation- 
ship and  showed  that  the  value  for  the  reduced  pressures  is 
the  same  for  all  substances  and  is  0.08846.  The  substances 
at  their  boiling  point  are  under  corresponding  states,  and  the 
value  of  the  ratio  of  the  boiling  temperature  to  the  critical 
temperature  is  about  0.75.  If  the  substance  is  under  cor- 
responding pressure  and  temperature,  the  volume  is  also  a 
corresponding  volume.  This  is  emphasized  by  the  data 
given  in  Table  XIII. 

TABLE  XIII  —  REDUCED  VALUES  IN  CORRESPONDING  STATES 

(COMPILED  FROM  YOUNG'S  STOICHIOMETRY) 
Ratio  of  Pressure  to  Critical  Pressure  =  0.08846 


SUBSTANCE 

£-• 

Tc 

V  "quid  =  » 

Hi!*.* 

Vc 

Acetic  Acid  
Benzene 

0.7624 

o  7282 

0.4100 

OAf)f\C 

254 

?8  i 

Carbon  Tetrachloride  .  .  . 
Ether  

0.7251 

o  7380 

O.4O78 

O  J.O^O 

20.3 

2745 
28  a 

Ethyl  Acetate  
Ethyl  Alcohol 

0.7504 

O  77Q4. 

0.4001 
o  4.061 

4O.J 

30.25 

Ethyl  Formate  

O  7^8^ 

O  AOO1 

o^-1  o 
2Q  6 

Methyl  Acetate  .... 
Methyl  Alcohol  
Methyl  Formate  .... 
Stannic  Chloride  .... 

°-7445 
0-7734 
0.7348 

0-7357 

0.3989 

0-3973 
0.4001 
0.4031 

30.15 

34-35 
29-3 

28.15 

The  data  confirm   van   der  Waals'  generalization  that : 
"  When  the  absolute  temperatures  of  two  substances  are 


*'. 
1 10  PHYSICAL  CHEMISTRY 

proportional  to  their  absolute  critical  temperatures,  their 
vapor  pressures  will  be  proportional  to  their  critical  pres- 
sures, and  their  orthobaric  (the  volume  of  a  liquid  at  a  given 
temperature  and  under  a  pressure  equal  to  the  vapor  pres- 
sure) volumes,  both  as  a  liquid  and  vapor,  to  their  critical 
volumes." 


CHAPTER  XI 
THE   PHYSICAL  PROPERTIES   OF   LIQUIDS 

MOLECULAR  VOLUME 

KOPP  (1858)  showed  that  it  is  possible  to  calculate  the 
volume  of  one  gram-molecule  of  a  liquid  organic  substance 
at  its  boiling  point  from  its  composition. 

Molecular  volume  equals  the  specific  volume  times  the 
molecular  weight ;  that  is, 

•A,  j      7         r  Molecular  weight 

Molecular  volume  = — 

density 

or  mol.  vol.  =  — 

p 

Kopp  selected  their  boiling  points  as  his  condition  for 
comparing  substances.  The  question  arises,  was  he  justified 
in  selecting  this  particular  condition,  and  if  so,  then  the 
boiling  temperatures  must  represent  corresponding  states 
and  consequently  corresponding  temperatures.  If  the  boil- 
ing points  are  reduced  temperatures,  his  selection  of  the  boil- 
ing temperatures  has  been  justified.  • 

Guldberg  .(1890)  and  Guye  (1890)  both  showed  that  the 
boiling  temperature  at  atmospheric  pressure  is  about  two 
thirds  of  the  critical  temperature  expressed  on  the  absolute 
scale.  We  have  just  seen  that  the  work  of  Young  presented 
in  Table  XIII  confirms  this  and  that  the  boiling  tempera- 
ture of  liquids  is  a  reduced  temperature  and  that  the  sub- 
stances at  their  boiling  points  are  at  corresponding  states. 

in 


112 


PHYSICAL   CHEMISTRY 


Kopp  determined  the  molecular  volume  of  a  number  of 
liquids  at  their  boiling  points  and  drew  the  following  con- 
clusions : 

1.  Among  homologous  compounds,  the  same  difference  of 
molecular  volume  corresponds  to  the  same  difference  of  com- 
position. 

2.  Isomeric  liquids  have  the  same  molecular  volume. 

3.  By  replacing  two  atoms  of  hydrogen  by  one  atom  of 
oxygen  the  molecular  volume  is  unchanged. 

4.  An  atom  of  carbon  can  replace  two  atoms  of  hydrogen 
without  change  of  volume. 

The  first  conclusion  stated  above  is  illustrated  in  Table 
XIV,  where  m  =  molecular  weight,  v  the  specific  volume, 

v  =  -  ,  where    p  =  the    density.      The    molecular    volume 
P 


m 


TABLE  XIV 


m 

Vm 

DIFFERENCE 

Methyl  alcohol 

CH3OH     .     i 

32 

39-4 

Ethyl  alcohol 

CaHsOH    .     . 

46 

57-1 

177 

,i    •, 

Propyl  alcohol 

C3H7OH    .     . 

60 

73-4 

10.3 

if.  e 

Butyl  alcohol 

C4H9OH    .     . 

74 

89.9 

10.5 
if.  ? 

Amyl  alcohol 
Hexyl  alcohol 

C5HnOH        . 
CeHiaOH        . 

88 

102 

1  06.  i 
122.5 

16.4 
1-2 

Heptyl  alcohol 

C7H15OH        . 

116 

138.7 

Octyl  alcohol 

C8Hi7OH        . 

130 

154-9 

lf\  ? 

Nonyl  alcohol 

C9H19OH  '     . 

144 

171.1 

The  difference  in  composition  of  these  compounds  is  CH2, 
which  makes  a  difference  in  the  molecular  volume  of  16.2 
units,  under  the  given  conditions,  while  under  other  condi- 
tions the  value  for  a  constant  difference  in  composition  may 
be  different. 


THE   PHYSICAL  PROPERTIES  OF  LIQUIDS 


In  his  later  more  accurate  investigations  Kopp  found  the 
value  for  CH2  in  two  homologous  series  as  given  in  Table  XV. 

TABLE  XV 


MOLECULAR 
VOLUME 

DIFFERENCE 

Formic  acid            H  COOH      .     .     . 

41.8 

Acetic  acid             CH3  COOH       .     . 

63.5 

21.7 

Propionic  acid        C2H5  COOH      .     . 

854 

21.9 

O  T     O 

Butyric  acid           C3H7  COOH      .     . 

106.6 

£  1  *£ 

Valeric  acid            C4H9  COOH      .     . 

130.3 

237 

Ethyl  formate        H  COOC2H5      .     . 

854 

oo  o 

Ethyl  acetate         CH3  COOC2H6 

107.6 

yy»m 

TQ  ? 

Ethyl  propionate  C2H5COOC2H5 

125.8 

1  O.^ 

Ethyl  butyrate      C3H7COOC2H6       . 

149.1 

23-3 

From  this  he  concluded  that  the  value  of  CH2  is  equal 
to  22.  He  also  found  that  by  replacing  2  C  by  4  H,  or 
C  by  2  H,  the  molecular  volume  did  not  change.  That 
is,  CH2  would  be  equivalent  then  to  2  C  =  22,  therefore 
C  =  ii  and  2  H  would  =  n  and  H  =  5.5.  In  this  man- 
ner the  atomic  volumes  of  other  elements  were  obtained  and 
the  following  values  have  been  assigned  :C=n;H  =  5.5; 
O  =  1 1 .  It  would  follow  from  this  that  the  molecular  vol- 
ume would  be  the  sum  of  the  atomic  volumes  just  as  the 
molecular  weight  is  the  sum  of  the  atomic  weights.  Hence, 
it  follows  that  isomeric  bodies  would  have  the  same  molec- 
ular volume.  Methyl  acetate,  CH3COOCH3,  Boil.  Pt.  57.1°, 
has  a  molecular  volume  of  84.8,  while  for  ethyl  formate, 
HCOOC2HB,  Boil.  Pt.  54.3°,  the  molecular  volume  was 
found  to  be  the  same,  85.4.  Hence  the  molecular  volume 
is  an  additive  property.  However,  in  attempting  to  calcu- 
late the  molecular  volume  from  the  atomic  volumes  it  was 
found  that  for  compounds  of  different  types  there  was  a 
marked  consistent  discrepancy  between  the  observed  and 


*;•, 
114  PHYSICAL  CHEMISTRY 

the  calculated  volumes.  This  fact  led  Kopp  to  assign  dif- 
ferent values  to  the  same  element,  depending  upon  the 
influence  of  the  nature  of  the  atom  and  its  linking  or  archi- 
tectural relation  to  the  other  atoms.  Hence  there  was  a 
constitutive  relation  which  had  to  be  taken  into  consideration 
which  demonstrated  that  this  property  is  not  strictly  additive. 
Kopp  found  that  for  oxygen  singly  linked,  as  in  the  hy- 
droxyl  group  (OH),  the  value  of  the  atomic  volume  is  7.8, 
while  for  doubly  linked  oxygen,  in  the  carbonyl  group  (CO) 
it  is  12.2.  On  this  basis,  the  calculated  values  for  forty-five 
different  compounds  did  not  vary  more  than  four  per  cent. 
Kopp  gives  the  following  values  for  the  elements : 

C      . n.o  Cl 22.8 

O  (OH) 7.8  Br  .     .    ..    ,    ".     .     .  27.8 

O  (CO) 12.2  I  ...  V.     .'".;'  37.5 

H 5-5  S  ,     .    ,     .    ,     .    .  22.6 

Sulphur  and  nitrogen  show  variations  similar  to  oxygen; 
they  have  different  values  in  some  different  types  of  com- 
pounds;  in  ammonia,  N  =  2.3,  in  the  cyanogen  group, 
CN,  it  =  28,  and  in  the  nitro  group,  NO2,  it  =  33,  which, 
shows  great  variations  in  the  value  of  the  nitrogen. 

Schroeder,  as  well  as  Kopp,  suggested  that  the  atomic 
volume  of  different  elements  is  the  same  or  some  multiple 
of  the  same  number,  which  unit  is  called  a  stere,  the  value 
of  which  was  between  6.7  and  7.4.  Later  Buff  (1865) 
showed  that  unsaturated  elements  gave  higher  values  than 
saturated  ones ;  that  is,  a  correction  had  to  be  made  for  the 
double  bond,  which  was  estimated  at  about  fojir  units. 
But  in  the  case  of  the  paraffins  aaid  their  corresponding 
defines  this  value  of  the  double  bond  is  practically  nil. 

The  formation  of  ring  compounds  results  in  the  decrease 
in  the  molecular  volume.  By  comparing  the  values  in  Table 
XVI  for  the  homologous  series  of  paraffins  with  the  cyclo- 
paraffins,  which  differ  by  2  H,  Willtstatter  (1907)  showed  the 
effect  of  the  ring  structure. 


THE   PHYSICAL  PROPERTIES  OF  LIQUIDS  115 

TABLE  XVI 


PARAFFIN 

Vm  AT  0° 

CYCLOPARAFFIN 

Vm  AT  0° 

DIFFERENCE 

Butane      . 

96.5 

Cyclobutane    .     .     . 

79 

17-5 

Pentane     . 

112.4 

Cyclopentane       .     . 

91.1 

21-3 

Hexane      .     .     . 

127.2 

Cyclohexane    .     .     ... 

105.2 

22.O 

Heptane    . 

142.5 

Cycloheptane 

118.0 

24-5 

Octane 

158.3 

Cyclooctane     .     .     . 

130.9 

27.4 

Nonane     .     .     . 

174-3 

Cyclononane    .     *    * 

159-5 

14.8 

If  the  value  for  2  H  be  deducted  from  the  differences,  it 
is  apparent  that  the  ring  formation  is  accompanied  by  a 
marked  contraction. 

More  recently  Ramsay,  Thorpe,  and  Lessen,  as  well  as 
Schiff,  have  worked  over  the  old  data  and  collected  new 
evidence  which  confirms  in  general  Kopp's  law  and  his  first 
approximations. 

SURFACE  TENSION  OF  LIQUIDS 

Within  a  liquid  a  molecule  is  attracted  equally  in  all  di- 
rections by  those  near  it,  and  this  force  diminishes  rapidly 
as  the  distance  from  the  molecule  increases.  It  is  apparent 
that  this  attractive  force  must  be  uniform,  since  there  is  no 
accumulation  of  the  molecules  of  the  liquid  in  one  portion ; 
i.e.  the  densities  of  all  portions  of  the  liquid  are  the  same. 

As  we  approach  the  surface  of  a  liquid  the  attraction 
from  above  diminishes  and  the  tension  from  the  sides  increases. 
This  increased  tension  along  the  surface  in  all  directions  is 
much  greater  than  that  between  the  molecules  in  the  in- 
terior of  the  liquid.  The  resultant  of  these  forces  is  normal 
to  the  surface  inward  and  not  outward,  which  results  in  a 
tendency  for  the  molecules  to  be  drawn  into  the  liquid  with 
a  corresponding  decrease  in  the  surface.  This  force  acting 
along  the  surface  and  tending  to  decrease  the  volume  is 


Il6  PHYSICAL   CHEMISTRY. 

designated  the  surface  tension,  and  hence  the  unit  surface 
tension,  y,  of  a  liquid  is  the  force  acting  at  right  angles 
to  a  line  one  centimeter  in  length  along  the  surface  of  the 
liquid.  The  molecules  on  the  surface  must  have  more  en- 
ergy than  those  on  the  interior,  and  this  increase  in  energy 
expressed  in  ergs  per  square  centimeter  of  surface  is  nu- 
merically equal  to  the  surface  tension  expressed  in  dynes  per 
linear  centimeter. 

The  surface  tension  may  be  determined  from  the  height 
to  which  the  liquid  will  rise  in  a  capillary  tube. 

Let  h  =  height  in  centimeters  that  the  liquid  rises, 
r  =  radius  of  the  capillary  tube, 
y  =  surface  tension,  expressed  in  dynes  per  centimeter. 

The  length  of  contact  of  the  surface  of  the  liquid  with  the 
inner  surface  of  the  tube,  multiplied  by  the  tension  per 
centimeter,  gives  the  total  force  acting,  i.e.  =  2 wry;  but 
this  is  equivalent  to  supporting  a  column  of  liquid  of  height 
h,  and  density  p,  against  the  force  of  gravity.  Therefore 
we  have 

7rr2gph  =  2irry 

Solving  for  y  we  then  have 

= 

which  is  expressed  in  absolute  units. 

The  surface  tension  decreases  with  the  rise  in  temperature, 
and  vanishes  at  the  critical  point. 

Ramsay  and  Shields  (1893)  employed  the  surface  tension 
of  liquids  for  the  determination  of  molecular  weights  of  pure 
substances  in  the  liquid  state,  which  was  an  extension  of 
the  earlier  work  of  Eotvos  (1886). 

In  the  gas  equation  pV  =  RT,  pV  may  be  termed  the 
volume  energy  of  the  gas,  and  it  was  shown  by  Eotvos  that 
a  similar  equation  expresses  the  relation,  within  certain 


THE  PHYSICAL   PROPERTIES   OF  LIQUIDS  117 

limits,  between  the  surface  energy  of  the  liquid  and  the 
temperature,  which  is 

yV*  =  k(tQ-t) 

in  which  y  =  surface  tension,  tQ  =  temperature  at  which 
yV%  =  o,  /  =  temperature  of  observation,  and  V  =  molec- 
ular volume  which  is  equivalent  to  mv.  If  mv  =  volume 
of  a  cube,  then  the  area  of  one  of  the  faces  is  (mu)*,  and 
since  the  molecular  volumes  contain  the  same  number  of 
molecules,  the  molecular  surface  (w»)»  or  V*  would  have 
an  equal  number  of  molecules  distributed  on  it. 

Experimentally  the  temperature,  /0,  was  found  to  coin- 
cide practically  with  the  critical  temperature,  i.e.  to  =  te. 
If  we  define  r  =  tc—t,  then  it  is  apparent  that  r  is  the 
temperature  measured  downward  from  the  critical  temper- 
ature. We  may  then  write  our  equation 

yV*  =  kr 

and  as  V*  =  surface  (s)  over  which  a  definite  number  of 
molecules  are  distributed,  substituting  we  have 

y  •  5  =  kr. 

Ramsay  and  Shields,  from  carefully  determined  surface 
tension  measurements  over  the  whole  range  of  temperatures 
up  to  the  critical  temperature,  showed  that  this  equation 
holds  only  approximately.  By 
plotting  the  values  of  y  •  5  against 
temperatures  (t)  we  have  the  curve 
represented  in  Fig.  9.  At  tc  =  t, 
r  =  o  and  y  •  5  =  o ;  but  at  lower 
temperatures,  T  increases  and  the 
values  of  y  •  5  are  represented  by 


ABC,  a  portion,  AB,  being  curved 

and  the  remainder,  BC,  being   a   straight  line.     Hence   at 

temperatures  represented  by  A  A'  the  equation  does  not 


Il8  PHYSICAL  CHEMISTRY 

hold,  but  beyond  a  certain  distance  from  the  critical  point 
it  does  hold. 

Ramsay  and  Shields  suggested  that  a  correction  for  this 
be  introduced  and  that  we  begin  to  count  from  a  point  A'. 
Making  this  correction  for  the  distance  d  represented  by 
A  —  A',  the  equation  becomes 

y  .  s  =  k(r-d). 

The  value  of  d  is  usually  6. 

This  formula  may  be  rewritten  thus  : 

y(mv)%  =  k(r-d). 

In  order  to  obtain  the  value  of  the  constant  k,  measure- 
ments of  the  surface  tension  will  have  to  be  made  at  two 
temperatures.  Then  for  simultaneous  values  we  have 

yi(mvi)%  =  kfa—d)  and 
y2  ( 
Solving  for  k  we  have 


Substituting  the  values  obtained  by  Ramsay  and  Shields 
and  solving  for  k,  the  following  results  were  obtained  : 

k 

Ether      .     .     .".'..     .......  2.1716 

Methyl  formate    ..........  2.0419 

Ethyl  acetate        ....'•  ......  2.2256 

Carbon  tetrachloride     ........  2.1052 

Benzene       ............  2.1043 

Chlorbenzene        .....  x  .....  2.0770 

Average    ...........  2.1209 

Hence,  using  the  molecular  weight,  m,  of  the  substance 
in  the  gaseous  state,  they  conclude  that  the  constant  k  is 
2.12  (C.G.S.  units)  for  normal  liquids  whose  molecular  aggre- 
gate is  the  same  in  the  liquid  as  in  the  gaseous  state.  That 


THE   PHYSICAL   PROPERTIES   OF  LIQUIDS  1  19 

is,  it  holds  for  non-associated  liquids.  It  follows  that  if  a 
liquid  gives  a  value  of  the  constant  2.12,  or  more,  it  is  non- 
associated,  and  if  less,  it  is  associated  ;  hence  we  have  a 
method  of  determining  the  degree  of  association  by  deter- 
mining the  relation  of  the  found  value  of  k  and  the  value  2.12 
for  normal  liquids. 

If  x  =  the  number  of  molecules  in  the  associated  molecule, 
m%  =  number  of  times  the  mass  of  the  associated  molecule 
is  greater  than  that  of  the  unassociated  molecule. 
Our  equation  would  then  be 


y  (mxv)*  =  2.i2(r  —  d)  (l) 

but  from  the  data  we  would  obtain 

y(mv)\  =  k^r-d).  (2) 

Dividing  (i)  by  (2)  we  have 


)  (3) 

in  which  x  is  termed  the  association  factor  and  represents  the 
number  of  gaseous  molecules  combined  to  form  the  liquid 
molecule. 

Morgan  has  worked  out  the  practical  details  by  means 
of  which  the  proportionality  of  the  surface  tension  of  a 
liquid  to  the  weight  of  a  falling  drop  of  it  can  be  determined. 
This  relationship  is  known  as  Tale's  Law.  Morgan  substi- 
tuted the  weight  of  the  drop,  falling  from  a  fine  capillary 
tube,  for  the  surface  tension  of  the  drop  and  obtained  the 
following  equation  : 

w(mv)%  =  k(r—d) 

where  k  is  established  by  using  the  non-associated  ^liquid 
benzene. 

Walden  makes  use  of  the  term'  specific  cohesion  (a2)  which 

he  defines  as  a2  =  ^  ,  where  y  is  the  surface  tension  and 
P 


120  PHYSICAL   CHEMISTRY 

p,  the  density.  If  the  surface  tension  is  measured  at  the 
boiling  point  of  the  liquid,  Walden  finds  a  relation  existing 
between  the  latent  heat  of  vaporization  and  the  specific 

cohesion,  which  is  expressed  thus  :  —  -=  constant,  where  L9  is 

a? 

the  latent  heat  of  vaporization  at  the  boiling  point.  The 
average  value  of  this  constant  is  given  as  17.9.  Trouton 
showed  that  the  latent  heat  of  vaporization,  L,,  multiplied 
by  the  molecular  weight,  m,  was  proportional  to  the  boil- 
ing 'point  of  the  liquid  measured  on  the  absolute  scale;  i.e. 

^—  *  =  constant.     This  is  known  as  Trouton's  Law,  which 

emphasizes  that  the  boiling  points  of  liquids  are  correspond- 
ing states,  and  hence  we  are  justified  in  using  these  tem- 
peratures as  comparable  temperatures,  and  as  the  boiling 
points  are  approximately  the  same  fraction  of  the  critical 
values,  they  are  reduced  temperatures.  Walden  empha- 
sized this,  too,  when  he  obtained  for  a  large  number  of  liquids 
20.7  as  the  value  of  the  constant  for  the  equation  repre- 
senting Trouton's  Law. 

As  —  *  =  constant  =17.9  (i) 


and  =  20.6  (2) 

solving  for  m  we  have 

_  20.6  T  _  1.16  T 
17.90?          a2 

from  which  the  molecular  weight  can  be  calculated. 

Using  this  formula  Walden  has  calculated  the  molecular 
weight  of  a  large  number  of  substances  and  found  the  usual 
formula  to  represent  the  substance  in  the  liquid  state,  such 
as  SnCl4,  SiCl4,  CC14,  PC13,  CSs,  etc. 

He  extended  his  formula  and  showed  that  it  is  applicable 
to  the  melting  point  of  substances  and  that  this  temperature 


THE  PHYSICAL  PROPERTIES  OF  LIQUIDS  1 21 

is  also  a  reduced  temperature  and  consequently  a  com- 
parable temperature.     The  formula  takes  the  form 


m 


From  this  fused  salts  appear  to  be  highly  associated,  for  he 
obtained  for  sodium  chloride  (NaCl)io,  for  sodium  bromide 
(NaBr)g,  and  for  sodium  iodide  (Nal)6.2,  as  the  respective 
formulae  representing  the  molecules  in  the  solid  state. 

NOTE.  —  See  Appendix  for  further  discussion  of  the  relative  surface 
tension  and  association  factors. 


CHAPTER  XII 
REFRACTION   OF  LIGHT 

THE  refraction  of  light  furnishes,  for  transparent  liquids, 
a  set  of  physical  constants  which  may  be  conveniently  and 
accurately  measured.  When  a  ray  of  light  passes  from  one 
medium  into  another,  the  direction  of  the  entering  ray  (the 
incident  ray)  changes  at  the  surface  separating  the  two 
media,  and  will  pass  into  the  other  medium  as  the  refracted 
ray.  The  angle  this  refracted  ray  makes  with  the  normal 
to  the  surface  of  separation  is  called  the  angle  of  refraction, 
and  the  angle  the  incident  ray  makes  with  the  normal  to 
the  surface  is  termed  the  angle  of  incidence.  The  refracted 
ray  lies  in  the  plane  of  incidence  and  on  the  opposite  side  of 
the  normal  to  the  incident  ray. 

Let  the  surface  of  separation  of  the  two  media  be  repre- 
sented by  AB  in  Fig.  10,  the  incident  ray  by  bo,  the  re- 
fracted ray  by  oc  and  the  normal  to 
the  surface  by  aod,  while  i  is  the  angle 
of  incidence,  and  r  is  the  angle  of  re- 
fraction. Then  sin  i  =  -^  and  sin  r  = 

bo 

£dj0r*™A  =  ri,   Since   bo   and  co  are 
co         sin  r       cd 

radii  of  the  circle.     This  ratio,  which  is 
termed  the  relative  index  of  refraction,  is  designated  by  «, 

j  sin  i 

and  we  have  n~  - — . 

sin  r 

That  is,  the  sine  of  the  angle  of  refraction  bears  a  constant 


REFRACTION  OF  LIGHT  123 

ratio  to  the  sine  of  the  angle  of  incidence.  This  is  Snell's 
Law.  The  numerical  value  of  this  ratio  depends  on  the 
nature  of  the  two  media  and  on  the  character  of  the  incident 
ray. 

According  to  the  wave  theory  of  light,  this  ratio  of  the 
sines  of  the  angles  of  incidence  and  of  refraction  is  the  same 
as  the  ratio  of  the  velocities  with  which  the  light  wave  trav- 
erses the  two  media.  The  absolute  index  of  refraction  is 
the  value  for  light  passing  from  a  vacuum  and  would  be 
slightly  higher  than  the  value  for  air ;  but  this  correction  is 
rarely  made. 

In  the  determination  of  the  index  of  refraction  of  liquids, 
we  have  the  passage  of  a  ray  of  light  through  the  liquid  into 
the  glass  prism  and  then  into  the 
air,  that  is,  we  have  the  passage 
of  the  ray  through  the  glass  prism. 
In  the  Pulfrich  refractometer,  which 
is  one  of  the  principal  ones  in  use, 
the  entering  ray  of  light  is  adjusted 
so  as  to  pass  horizontally  between 
the  liquid  and  the  prism,  and  the 
angle  of  incidence  then  becomes 

90°.  If  a  ray  of  light  be  allowed  to  enter  the  prism  as  is 
indicated  in  Fig.  n,  it  will  be  refracted  as  it  passes  into 
the  glass  from  the  liquid  and  again  as  it  passes  from  the 
glass  into  the  air,  where  it  is  observed  by  means  of  the 
telescope  of  the  instrument.  We  desire  an  expression  for 
the  index  of  refraction  between  the  air  and  the  liquid  as  it 
is  customary  to  define  the  ratio  when  the  ray  passes  from 
air  into  the  denser  medium.  For  these  three  media  we 
would  have  the  following  relations : 

liuid    ,r         air      .-,        N        air 
;  N  =  —  - ,  then  —  = 


glass  '  glass '  n\      liquid 

which  we  shall  designate  by  n. 


••• 

124  PHYSICAL   CHEMISTRY 

Now  we  have 


and 


glass     sin  r  glass      sin  r' 

and  remembering  the  angle  of  incidence  is  90°,  then  we  have 

sin  90°  f  x 

«i  =     .      ,  (2) 

sin  r 

Since  sin  90°  =  i,  this  becomes 

sin  r' 
But  sin  r'  =  cos  r  =   Vi  —  sin2  r.  (4) 

Transposing  (i)  we  have  sin  r  =  ^P~^  (5) 

N 

Substituting  in  (4) 


Substituting  this  value  in  (3),  we  have 

i  N 


N 

N 
Substituting  in  n  =  —  ,  we  have 


n  =  VjV2  -  sin2  i. 
Therefore  the  index  of  refraction,  n  =  V N2  —  sin2  i. 

9 

The  value  of  N  is  usually  furnished  with  the  instrument,  and  tables 
are  provided  for  obtaining  the  value  of  n  for  any  observed  value  of  the 
angle  *". 

It  is  necessary  to  use  monochromatic  light,  as  light  of 
different  wave  lengths  is  differently  refracted  and  conse- 
quently gives  different  indices  of  refraction.  It  is  cus- 
tomary to  use  sodium  light,  the  D  line,  but  the  light  of  other 
elements  is  also  used,  such  as  that  of  lithium,  strontium,  or 
the  three  rays  of  the  hydrogen  spectrum :  the  red  line  Ha, 
the  blue  line  H/s,  and  the  violet  line  Hy. 


REFRACTION  OF  LIGHT 


125 


METHODS  OF  EXPRESSING  REFRACTIVE  POWER 

The  index  of  refraction  varies  with  the  temperature  and 
with  the  pressure,  in  general,  with  all  conditions  that  in- 
fluence the  density,  and  hence  efforts  have  been1  made  to 
find  an  expression  which  will  be  independent  of  these  various 
physical  factors  and  which  is  dependent  only  upon  the  chemi- 
cal nature  of  the  substance.  Gladstone  and  Dale  developed 


the  empirical  formula  r 


n 


,  and  named   this  r,  the 


specific  refractive  index  or  specific  refractivity. 

Lorentz  of  Leyden  proposed  (1880)  a  formula  deduced 
from  the  electromagnetic  theory  of  light, 


*r  — 


r  = 


Lorenz  of  Copenhagen  simultaneously  derived  the  same 
formula  deduced  from  the  undulatory  theory  of  light.  This 
formula  is  independent  of  temperature,  pressure,  and  change 
of;  state.  Table  XVII  represents  the  specific  refractivity  of 
water  at  different  temperatures  as  calculated  from  both 
formulae.  The  n2  formula,  as  it  is  termed,  apparently  gives 
more  constant  values : 

TABLE  XVII 


GLADSTONE  AND  DALE 

LORENTZ 

TEMPERATURE 

n—  i 

«2-I     £ 

P 

»*+2      p 

0° 

0.3338 

0.2061 

10 

0.3338 

0.2061 

20 

0.3336 

0.2061 

90 

0.3321 

0.2059 

IOO 

0.3323 

0.2061 

The  effect  of  the  change  of  state  is  shown  in  Table  XVIII. 
The  w2  formula  gives  more  uniform  values,  there  not  being 


126 


PHYSICAL   CHEMISTRY 


such  great  differences  between  the  value  of  the  vapor  and 
liquid  as  by  the  Gladstone-Dale  formula. 

TABLE  XVIII 


SUBSTANCE 

»- 

-i 

«2-I      i 

f 

i 

nH-2     p 

Temp. 

Vapor 

Liquid 

Dif- 
ference 

Vapor 

Liquid 

Dif- 
ference 

Water                 -     . 

10° 

'i  TOI 

-J-2-jg 

O  O2^7 

o  2068 

o  2061 

OOO7 

Carbon  bisulphide 

10 

•4347 

•4977 

.0630 

.2898 

.2805 

•0093 

Chloroform         .     .'    . 

10 

.2694 

.3000 

.0306 

.1796 

.1790 

.0006 

Molecular  refractivity  is  obtained  by  multiplying  the 
specific  refractivity  by  the  molecular  weight  (m)  of  the 
substance.  Our  formulae  then  become 


mr  = 


mr  = 


n  —  i 


m 


n 


2  _ 


m 


From  the  above  data  it  would  appear  that  there  is  no 
question  as  to  which  of  the  two  formulas  is  the  more  trust- 
worthy, but  all  data  do  not  give  such  conclusive  evidence, 
hence  there  is  still  a  difference  of  opinion,  and  the  workers 
in  Continental  Europe  use  the  formula  of  Lorentz-Lorenz, 
while  in  England  the  Gladstone- Dale  formula  is  employed. 
Most  of  the  data  have  been  calculated  by  means  of  the 
Lorentz-Lorenz  formula,  and  hence  this  is  the  one  more 
generally  used. 

The  first  systematic  study  of  the  refractivity  of  organic 
compounds  was  made  by  Gladstone  and  Dale  (1858-63). 
They  showed  that  "  Every  liquid  has  a  specific  refractivity 
energy  composed  of  the  specific  refractivity  energies  of  its 
component  elements  modified  by  the  manner  of  combination 


REFRACTION  OF  LIGHT 


I27 


and  which  is  unaffected  by  change  of  temperature."  Lan- 
dolt  (1864),  from  extensive  data,  confirmed  the  refractive 
values  for  the  elements  carbon,  hydrogen,  and  oxygen,  and 
showed  that  the  constitution  had  an  effect  on  the  refractivity. 
Bruhl  (1891)  extended  the  work  of  the  previous  investi- 
gators and  tabulated  the  following  values  for  the  refractivity 
constants. 

The  refractivities  of  the  commoner  elements  are  given  in 
Table  XIX  for  the  D  line,  and  the  hydrogen  lines,  Ha,  Hp, 
Hy,  and  also  the  dispersive  power  for  H/s  —  Ha  and  Hy  —  Ha. 
These  are  the  recalculated  values  of  Eisenlohr  and  are  prac- 
tically the  same  as  the  original  values  of  Bruhl  and  Conrady. 

TABLE  XIX 


ELEMENT 

Na 
D  LINE* 

Ha 

H, 

Hv 

V. 

Hv-Ha 

Carbon  C  

2  4.2 

2  4.1 

2  4.4. 

2  4.6 

o  025 

oo  6 

Hydrogen  H        
Oxygen  O'  in  hydroxyl     .     . 
Oxygen  O<  in  ether    . 
Oxygen  O"  in  ketone        .     . 
Chlorine  Cl    .    •.'.'. 

1.  10 
1.52 
1.64 
2.21 
5  Q6 

1.09 
1.52 
1.64 
2.19 

C  Q'J 

i.  ii 

1-53 
1-65 
2.24 
6  04 

1.  12 

1-54 
1.66 
2.26 
6  10 

0.023 

0.006 

0.012 
0.057 

o  107 

0.029 
0.015 
0.019 
0.078 
o  168 

Bromine  Br  

8  86 

8  80 

Q  OO 

QIC 

O  21  1 

o  ^4.0 

Iodine  I     .     .     .     .     .     .     . 
Double  Bond  =       .     .  '  ..     .- 
Triple  Bond  =    

13.90 

i-73 
2.40 

13-75 
1.68 

2-33 

14.22 

.1.82 
2.50 

14-52 

1.89 

2.53 

0.482 
0.138 
0.139 

0-775 

0.20O 
O.I7I 

Homologous  series  of  paraffin  compounds  with  a  difference 
of  CH2  have  a  difference  in  the  molecular  refractivity  of 
4.57,  therefore  the  value  of  CH2  =  4.57.  Landolt  found 
4.56.  The  value  fluctuates  between  4.58  and  4.61  for  dif- 
ferent series,  while  individual  values  show  even  greater  vari- 
ation, 4.11  to  4.86. 

The  data  in  Table  XX  show  the  value  for  CH2  in  a  number 
of  different  types  of  compounds  with  the  number  of  sub- 
stances investigated  in  each  series ; 


128 


PHYSICAL   CHEMISTRY 


TABLE  XX 

(After  Cohen) 


MI 

II 

Zz 

Ha 

Na 
D  LINE 

H0 

Hv 

DISPERSION 

H)8-H« 

Hv-Ha 

Hydrocarbons  .  . 
Aldehydes  and  ketones 
Acids 

66 
92 

74 
81 
190 
503 

4.6O 
4.60 
4-58 
4.6l 

4-58 

4-59 

4.62 
4.62 
4.61 
4-63 
4.60 
4.62 

4.67 
4.67 
4.66 
4.68 

4-65 
4.66 

4.72 
471 
471 
472 
4.69 
471 

0.072 
0.069 
0.070 
0.070 
0.069 
0.071 

O.II8 

O.II2 
O.II5 
O.II2 
O.I  1  1 
O.II3 

Alcohols  .... 
Esters  .  .  :  .  . 

Mean                   .     « 

Since  the  refractivities  of  the  individual  elements  are 
constant,  it  follows  that  the  molecular  refractivity  (M«)  of 
isomeric  substances  should  be  identical.  The  data  in 
Table  XXI  show  this  to  be  the  case : 

TABLE  XXI 
(After  Cohen) 


SUBSTANCE 

FORMULA 

Ha 

Ma 

My-Ma 

Propyl  alcohol  .... 
Isopropyl  alcohol 

C3H7(OH) 
C3H7(OH) 

0.2903 
0.2907 

1742 
1744 

0.41 
0.42 

Propyl  aldehyde  .... 
Acetone 

C3H6O 
C3H6O 

0.2747 

o  2767 

15-93 
I6.O5 

0.41 
O  d.'l 

Propionic  acid  .... 
Methyl  acetate  .... 
Ethyl  formate  .... 

C3H602 
C3H602 
C3H602 

0.2354 
0.2437 
0.2423 

1742 
18.03 
17-93 

0.42 
0.44 
0.44 

Butyl  alcohol  
Isobutyl  alcohol  .... 
Trimethyl  carbinol  . 
Ethyl  ether 

C4H9(OH) 
C4H9(OH) 
C4H9(OH) 
(C2H5)2O 

0.2974 
0.2967 
0.2985 

O^OI  5 

22.01 
21.96 
22.09 
22  "*I 

0.52 
0.51 
0-53 
O.55 

Butyl  iodide 

C4H9I 

0.1807 

-i-i  25 

1.26 

Isobutyl  iodide  .... 

C4HJ 

0.1807 

33-25 

1.26 

REFRACTION  OF  LIGHT 


I29 


TABLE  XXI  —  Cont. 


SUBSTANCE 

FORMULA 

Ha 

Ma 

My-Ma 

Isocaproic  acid     .... 

C6H1202 

0.2691 

31-22 

0-77 

Isoamyl  formate  .     .     .    ". 

C6H1202 

0.2729 

31.66 

0.77 

Ethyl  butyrate    .... 

C6H1202 

0.2690 

31.20 

0-75 

Methyl  isovalerate  .     .     . 

C6H1202 

O.27I2 

31.46 

0.78 

Ortho  xylene 

C  H 

O  77^O 

'IC    CJ 

C2 

Meta  xylene 

O  ^70 

-ZZ.JT. 

.54. 

Para  xylene     

C8H10     *• 

0.3368 

35-70 

•56 

Ethyl  benzene      .     .     .     . 

CgHio 

0-3343 

3544 

•50 

Pseudo  cumene    .... 

CgHi2 

0.3363 

40.35 

.69 

Mesitylene      ..... 

CgHi2 

0.3361 

40.33 

•63 

Determination  of  the  doubly  linked  oxygen,  O",  was  ob- 
tained by  subtracting  from  the  molecular  refractivity  of  a 
series  of  aldehydes  or  ketones  (CnH2nO),  the  calculated 
value  of  (CH2)n.  The  value  obtained  was  2.32.  The  dif- 
ference between  the  molecular  refractivity  of  aldehydes 
and  acids  gave  the  value  for  hydroxyl  oxygen  (O').  The 
calculated  value  for  (CH2)nO"  subtracted  from  the  observed 
values  for  the  aliphatic  esters  gave  a  mean  value  of  1.65  for 
the  ether  oxygen  (O<).  Briihl  and  Conrady  obtained  the 
value  for  the  double  bond  by  deducting  the  constant  for  a 
saturated  carbon  from  the  observed  values  and  obtained 
1.63  to  2.17  with  a  mean  value  of  1.83. 

The  following,  Table  XXII,  according  to  Eykman,  gives 
the  values  for  a  number  of  different  types : 

TABLE  XXII 


No  radicals 

CH2  •  CH2 

i  5i 

One  radical        

RCH  :  CH2 

i.  60 

Two  radicals 

RCH  •  CHR 

I  75 

Three  radicals  

R2C  •  CHR 

i  88 

Four  radicals 

R2C  •  CR2 

2  OO 

130 


PHYSICAL   CHEMISTRY 


The  effect  of  simple  ring  formation  gives  very  small  values, 
not  much  greater  than  the  variations  due  to  experimental 
error.  Tschugaeff  from  a  large  amount  of  data  found  a 
value  of  about  MD  =  0.67,  while  Oesterling  found  nearly 
the  same  value  (MD  =  0.71).  These  values  were  used  to 
establish  the  cyclic  structure  of  various  compounds. 

Upon  the  basis  that  benzene  has  three  double  bonds,  the 
value  for  the  molecular  refractivity  may  be  calculated  as 
follows,  from  the  atomic  refractivities  given  in  Table  XIX, 
for  the  red  H  line,  Ha. 

.  • 

6  C  atoms  6  X  2.41  =  14.46 

6  H  atoms  6  X  1.09  =    6.54 

3  double  bonds  3  X  i  .68  =    5.04 

Sum  of  atomic  refractivities          26.04 

Experimentally  at  20°,  n  =  1.4967,  p  =  0.8799,  and  the 
molecular  weight  is  78. 

Substituting  in  the  n2  formula  we  have 

i.4o672  —  i  .        78 

-  x  — r-* =  25.93 

I.49672  +  2         0.8799 

which  is  a  close  agreement. 

Similarly,  some  of  the  other  simple  benzene  derivatives 
give  the  following  values  according  to  Cohen. 


M 

a 

Observed 

Calculated 

Benzene    ...                                    . 

2^  Q-l 

26  O4. 

Toluene     .... 

T.Q  7Q 

iO.8q 

Ethyl  benzene    '.    '. 
Phenol       .     „     .-'    *     .     .  -\'    .-    t     . 

3544 

27  75 

35-37 

27  82 

Benzyl  alcohol    i-   . 

^2.2^ 

32.^1 

Chlorobenzene    '-    . 

30.90 

31.22 

REFRACTION  OF  LIGHT  131 

The  following  complex  compounds  do  not  show  such  a 
close  agreement : 


Id 

a 

C      -        C-T*        VT^T. 

Observed 

Calculated 

Naphthalene       

4.-I.Q-Z 

4.1.65 

Anthracene    . 

61.15 

55-15 

Phenanthrene     

61.59 

56.99 

The  refractivity  is  employed  as  an  aid  in  deciding  the 
structural  relation  of  compounds. 

The  refractive  index  is  used  as  a  means  of  identifying  sub- 
stances, determining  the  purity  or  presence  of  adulterants, 
and  also  the  strength  of  solutions  or  concentration.  For 
analytical  purposes,  then,  the  index  of  refraction  is  a  property 
that  is  coming  into  very  general  use.  A  number  of  special 
types  of  instruments  are  being  employed  for  this  purpose, 
among  which  may  be  mentioned,  in  addition  to  the  Pulfrich 
refractometer : 

(1)  The  Abbe  refractometer,  which  has  a  scale  giving  the 
index  of  refraction  direct.     This  is  employed  extensively 
for  the  analysis  and  identification  of  oils. 

(2)  The  butyrometer  is  employed  for  analysis  of  butter 
fat  and  has  an  arbitrary  scale. 

(3)  The  Immersion  refractometer  is  employed  in  analy- 
sis  of    milk   serum   to   determine   whether   the   milk   has 
been  watered,  and  in  the  analysis  of  various  other  types  of 
solutions.     These  are  also  provided  with  an  arbitrary  scale, 
which  is   divided  into   100  arbitrary   divisions   comprising 
indices  from  1.325  to  1.367. 

(4)  The   Zeiss  refractometer  is  particularly  adapted  to 
determination  of  alcohol. 

The  greater  the  wave  length  of  light,  the  less  the  refractive 


132  PHYSICAL   CHEMISTRY 

index,  and  hence  the  index  of  refraction  varies  with  the 
kind  of  light  employed.  The  difference  between  the  spe- 
cific refractivities  for  light  of  greatly  different  wave  lengths 
is  called  the  specific  dispersive  power  or  dispersivity.  This  is 
obtained  by  using  either  of  the  -formulae  and  subtracting 
the  specific  refractivities. 

2  _ 


The  molecular  dispersivity  is  the  molecular  weight  (m) 
times  the  specific  dispersivity. 


z     p 

The  dispersivity  values  have  been  determined  in  a  man- 
ner similar  to  the  method  for  obtaining  the  refractivity  con- 
stants for  the  elements  and  the  different  linkages.  Bruhl 
concludes  that  dispersivity  is  preeminently  a  constitutive 
property  and  is  much  more  valuable  as  an  aid  in  establish- 
ing structural  relations  than  the  refractivity.  Eykman 
has  shown  that  dispersivity  affords  a  valuable  indication  of 
the  position  of  the  double  bond.  Auwers  and  Ellinger  have 
shown  that  dispersivity  is  increased  by  the  double  bond  in 
the  side  chain  as  compared  with  it  in  the  nucleus.  In  Table 
XIX  is  given  the  atomic  dispersive  power  of  a  number  of  ele- 
ments using  the  hydrogen  lines  and  in  Table  XXI  is  given 
the  molecular  dispersive  power  of  a  few  isomeric  compounds. 


CHAPTER  XIII 
OPTICAL  ROTATION 

ORDINARY  light  consists  of  transverse  vibrations  which 
take  place  in  all  directions  at  right  angles  to  the  direction  of 
the  ray.  If  a  ray  of  light  is  allowed  to  pass  through  a  piece 
of  tourmaline  (an  aluminium  boron  silicate)  cut  parallel  to 
the  crystallographic  axis,  a  part  of  the  light  will  pass  through. 
If  another  similar  piece  of  tourmaline  is  placed  with  its 
axis  parallel  to  the  first,  the  ray  of  light  will  pass  through 
this  second  piece  also.  If  this  second  piece  be  rotated  in  a 
plane  perpendicular  to  the  ray  of  light,  the  intensity  of 
the  light  will  gradually  diminish  with  the  rotation,  and 
when  the  axes  are  at  right  angles  the  light  which  passes 
through  the  first  tourmaline  plate  will  not  pass  through  the 
second  when  in  this  position.  Transverse  vibrations  in 
only  one  plane  pass  through  the  first  plate  of  tourmaline, 
and  the  light  which  comes  through  is  said  to  be  plane 
polarized. 

If  a  ray  of  light  be  allowed  to  pass  through  a  piece  of 
Iceland  spar  normal  to  one  of  the  faces,  it  will  be  broken  up 
into  two  rays  which  are  differently  refracted.  This  phe- 
nomenon is  termed  double  refraction,  and  the  two  rays  are 
designated  the  ordinary  ray,  which  follows  the  laws  of  refrac- 
tion, and  the  extraordinary  ray,  which  does  not  follow  these 
laws.  These  two  rays  are  polarized  at  right  angles  to  each 
other.  Hence  Iceland  spar  can  be  used  for  the  purpose  of 
obtaining  plane  polarized  light,  but  in  order  to  do  this  it  is 

133 


134  PHYSICAL   CHEMISTRY 

necessary  to  intercept  one  of  the  rays,  and  thus  permit  only 
one  to  pass  through.  This  may  be  done  by  taking  a  long 
crystal  of  Iceland  spar,  grinding  the  ends  so  as  to  change  the 
angle  about  three  degrees,  thus  making  the  angle  (Fig.  12) 
DAB  >  68°,  and  then  cutting  it  in  two  along  the  line  DB 
perpendicular  to  the  new  face  AD,  thus  making  the  angle 
ADB  a  right  angle.  These  cut  surfaces  are  then  polished 
and  cemented  in  their  original  position  by  Canada  balsam. 
£  The  ray  of  light  entering 

at  R  is  doubly  refracted, 
the  ordinary  ray  following 
the  law  of  refraction  is 
refracted  and  meets  the 
surface  of  Canada  balsam, 

which  has  an  index  of  refraction  of  1.55,  which  is  greater 
than  that  of  the  Iceland  spar,  1.48,  for  the  ordinary  ray. 
If  it  strikes  the  Canada  balsam  at  an  angle  greater  than  the 
critical  angle,  it  will  be  totally  reflected  at  the  surface.  The 
extraordinary  ray,  RE,  is  refracted  less  than  the  ordinary 
ray.  Its  index  of  refraction  in  the  medium  is  greater 
than  that  of  the  Canada  balsam,  consequently  it  can  never 
be  reflected  at  that  surface  and  so  will  pass  through  the 
prism  as  indicated  by  REE'.  At  the  point  of  entrance, 
R,  and  also  at  the  surface  where  the  two  pieces  are 
cemented  together,  the  extraordinary  ray  is  refracted,  but 
the  amount  is  so  small  that  on  a  diagram  of  this  size, 
it  can  hardly  be  represented  in  any  other  way  than  by  a 
straight  line  through  both  sections  of  the  prism.  This 
prism  is  known  as  a  Nicols  prism,  and  since  it  produces  plane 
polarized  light  it  is  known  as  a  polarizer.  The  plane  in  which 
the  plane  of  polarization  is  located  can  be  ascertained  by 
means  of  a  second  Nicols  prism ;  when  it  is  used  in  this 
manner  it  is  designated  an  analyzer. 

Method  of  Measuring  Optical  Rotation.  —  The  amount 
of  rotation  can  be  measured  by  placing  the  substance  be- 


OPTICAL  ROTATION  135 

tween  two  Nicols  prisms,  one  a  polarizer  to  produce  the 
polarized  light,  and  one  an  analyzer  to  determine  the  amount 
the  plane  of  polarization  has  been  rotated.  This  is  meas- 
ured by  having  a  scale  divided  into  degrees  and  fractions 
thereof  attached  to  the  analyzer  so  as  to  determine  the 
angle  through  which  the  analyzer  has  to  turn  in  order  to 
permit  the  light  to  pass  through.  Such  an  instrument  is 
called  a  polarimeter.  The  light  which  comes  through  would 
produce  either  a  bright  field  or  total  darkness  ;  in  either  case 
it  would  be  difficult  to  read  accurately.  In  order  to  obtain 
a  field  which  can  be  read  easily  a  number  of  devices  have 
been  designed  and  are  now  employed,  such  as  the  bi-quartz 
disk,  the  quartz  wedge  compensator,  and  the  Lippich  half- 
shadow  apparatus  consisting  of  small  Nicols. 

The  angle  of  optical  rotation  is  proportional  to  the  thick- 
ness of  the  liquid  through  which  the  light  passes.  The 
specific  rotation  is  the  angle  of  rotation,  «,  divided  by  the 
length,  I,  of  the  column  of  liquid  times  its  density,  p.  Since 
the  rotation  varies  with  the  temperature,  it  is  customary 
to  state  the  temperature  of  the  solution  at  which  the  deter- 
mination is  made  as  well  as  the  kind  of  light  used.  The 
equation  for  the  specific  rotation  is 


'  P 


in  which  /°  represents  the  temperature  and   D,   the  spec- 
trum line,  sodium  in  this  case. 

For  solutions  when  the  concentration  is  expressed  in  grams, 
g,  in  definite  volume,  v,  we  have 


[a]    =  ~    or,   for  concentration    in 

D 


per  cent,  p, 


136  PHYSICAL   CHEMISTRY 

The  molecular  rotation  of  liquids  would  be  expressed 

r  i'°      a  •  m 
m[«     =  7- 

J>  /  •  p 

or  it  is  sometimes  written 


and  owing  to  the  large  value  of  the  rotation  it  is  customary 
to  divide  the  result  by  100. 

Asymmetry.  —  It  was  early  recognized  by  Biot  that  many 
substances  in  aqueous  solutions  had  the  power  of  rotating 
the  plane  of  polarized  light,  while  an  explanation  was  offered 
through  the  classic  researches  of  Pasteur.  One  peculiarity 
of  compounds  and  their  solutions  which  manifest  optical 
activity  is  that  the  compounds  contain  one  or  more  asym- 
metric atoms  of  either  carbon,  nitrogen,  sulphur,  selenium, 
tin,  silicon,  etc.  In  fact,  there  is  no  authentic  case  in  which 
an  active  compound  has  been  found  that  does  not  contain 
an  asymmetric  atom.  That  is,  a  carbon  atom  is  said  to  be 
asymmetric  when  all  four  of  the  valences  are  satisfied  by 
groups  which  are  different  chemically  or  structurally.  For 
example,  amyl  alcohol,  which  is  optically  active,  may  be 
represented  by  the  formula  designated  active.  If,  however, 
the  OH  group  be  replaced  by  hydrogen,  we  obtain  the  formula 

CH3         H  CH3         H 

X      •    X 

C2HB         CH2OH  CsHg         CH3 

ACTIVE  INACTIVE 

designated  inactive,  and  the  groups  attached  to  the  carbon 
atom  are  not  all  different,  as  they  are  in  the  formula  marked 
active.  In  the  substitution,  however,  it  is  necessary  to 
destroy  the  asymmetric  character  of  the  carbon  atom  be- 
fore the  substance  will  become  inactive.  In  the  case  of 


OPTICAL   ROTATION  137 

malic  acid  (monohydroxysuccinic  acid)  and  of  tartaric  acid, 
there  are  four  different  groups  attached  to  the  asymmetric 
carbon  atoms  as  the  following  formulas  indicate : 

H  H 

I  I 

OH— C— COOH  OH— C— COOH 

I  I 

H— C— COOH  OH— C— COOH 

i         i     i 

MALIC  ACID  TARTARIC  Acir 

These  active  compounds  have  isomers  which  have  anal- 
ogous properties,  and  while  they  are  both  optically  active, 
and  the  rotation  is  of  the  same  magnitude,  it  is  in  opposite 
directions  for  the  two  compounds,  one  rotating  the  plane  of 
polarized  light  to  the  right,  and  the  other  rotating  it  to  the 
left.  Those  that  rotate  the  plane  of  polarized  light  to  the 
right  are  termed  dextro-rotatory,  and  those  that  rotate  the 
plane  of  polarized  light  to  the  left  are  termed  Icevorotatory. 

In  1867,  Kekule  proposed  that  the  carbon  be  conceived  as 
located  at  the  center  of  a  regular  tetrahedron  and  that  the 
four  affinities  be  represented  by  lines  drawn  to  the  four 
vertices.  For  convenience  of  writing,  the  symbol  for  car- 
bon is  omitted  and  the  elements  or  groups  in  combination 
with  the  carbon  are  indicated  at  the  vertices,  as  shown  in 
the  following  figures.  In  order  to  explain  isomerism,  Le 
Bel  and  van't  Hoff  simultaneously  (1874)  and  independently 
made  use  of  the  idea  of  the  tetrahedron  carbon  atom  and 
grouped  the  elements  or  groups  in  combination  with  the 
carbon  atom  around  the  base  of  the  tetrahedron  in  one  di- 
rection to  represent  one  isomer  and  in  the  opposite  direction 
to  represent  the  other  isomer.  This  is  illustrated  in  Fig. 
13,  where  we  have  in  I  the  symbols  acd  arranged  from 
right  to  left,  while  in  II  they  are  arranged  from  left  to  right. 
The  rotation  would  be  represented  as  —  or  laevorotatory 


138 


PHYSICAL   CHEMISTRY 


FIG.  13. 


in  I  and  +  or  dextro-rotatory  in  II.  These  two  figures,  1 
and  II,  are  the  mirrored  images  of  each  other,  and  while 
they  are  alike,  they  cannot  be  superposed ;  that  is,  they  are 

right-handed  and  left-handed.  It 
is  known  that  solutions  of  two 
isomeric  compounds  can  be  mixed 
in  equal  quantities  so  as  to  produce 
an  inactive  mixture,  and  such  mix- 
tures are  termed  racemic  mixtures. 
There  are,  however,  certain  forms 
of  isomeric  active  compounds  which  are  inactive,  and  this 
property  is  explained  upon  the  assumption  that  by  an  internal 
compensation  the  compound  is  rendered  inactive.  Such  in- 
active compounds  are  designated  the  meso  form.  Here  we 
have  an  illustration  of  a  compound  containing  an  asymmetric 
carbon  atom  without  rendering  the  compound  optically  active. 
In  the  case  of  tartaric  acid  we  have  the  example  of  a 
compound  existing  in  these  three  forms,  and  in  Fig.  14  is 
illustrated  the  structural  arrangements  by  means  of  which 
they  are  explained. 

COOH  COOH  COOH 

H— C— OH  OH— C— H 


H— C— OH 

I 
CQOH 


H— C— OH 

HO— C— H 
I 
COOH 


MESOTARTARIC  ACID 


L^VOTARTARIC  ACID 
FIG.  14. 


DEXTROTARTARIC  ACID 


OPTICAL  ROTATION  139 

The  meso  form  manifests  no  rotation,  the  laevotartaric  acid 
rotates  the  plane  of  polarized  light  to  the  left,  and  the  dextro- 
tartaric  acid  rotates  the  plane  of  polarized  light  to  the  right. 
In  addition,  we  have  the  racemic  acid,  which  is  a  mixture  of 
equimolecular  parts  of  /-  and  of  d-tartaric  acids. 

Many  substances  are  optically  active,  and  the  specific 
rotation  of  these  is  listed  in  tables  of  physical  constants. 
The  use  of  this  property  is  one  of  the  principal  methods 
employed  in  identifying,  testing  the  purity,  as  well  as  making 
quantitative  determinations  of  such  substances  as  sugars  ; 
essential  oils,  including  lemon,  wintergreen,  peppermint, 
etc.  ;  the  alkaloids,  nicotine,  brucine,  strychnine,  etc.  ;  tur- 
pentine, camphor,  and  a  long  list  of  others.  In  the  case 
of  sugars,  this  method  is  generally  employed,  as  the  rotation 
is  proportional  to  the  concentration  : 


in  which  c  equals  concentration  in  100  cc.  of  solution.  Then 
a  =  [a]/  •  c,  and  since  a  tube  of  constant  length,  /,  expressed 
in  decimeters,  is  employed,  and  the  specific  rotation  of 
cane  sugar  is  constant,  [a]  =  (66.5,  /  =  one  decimeter)  ; 
substituting  we  have  a  =  66.5-  /•  c,  but  66.5  /  is  a  constant, 
fc,  then  a  =  kc,  the  rotation  is  proportional  to  the  concen- 
tration. In  Table  XXIII  are  given  the  values  of  the  specific 
rotation,  [a]2°,  at  20°  for  sodium  light,  the  D-line  of  the 
spectrum,  for  the  carbohydrates  commonly  occurring  in 
foods.  These  values  are  the  ones  usually  employed  in  ana- 
lytical work  and  are  sufficiently  exact  for  that  purpose. 

Effect  of  Temperature.  —  We  have  seen  that  the  temper- 
ature affects  the  specific  rotation,  and  the  formula  contains 
a  term  designating  the  temperature  at  which  the  deter- 
mination is  made.  The  rotation  may  increase  or  decrease 
with  the  change  of  temperature.  Methyl  tartrate  is  prac- 
tically inactive  at  o°  C.,  while  below  this  temperature  it  is 


140 


PHYSICAL  CHEMISTRY 


laevorotatory,  i.e.  negative.  Many  of  the  esters  of  tar- 
taric  acid  pass  through  a  maximum  value  for  the  specific 
rotation  with  change  of  temperature,  while  some  of  those 
with  large  negative  rotation  change  but  little  with  a  large 
change  in  temperature.  For  most  sugars  the  specific  ro- 
tation is  practically  constant  for  all  temperatures.  In 
general,  however,  the  specific  rotation  decreases  with  the 
temperature,  as  is  shown  by  laevulose  and  arabinose,  par- 
ticularly while  xylose  increases  and  dextrose  remains  prac- 
tically constant  for  temperature  changes  up  to  100°.  It  is 
necessary  to  determine  the  temperature  accurately  in  all 
sugar  analysis  and  to  make  the  necessary  corrections. 
Browne  has  compiled  formulae  by  which  such  corrections 
can  be  made  and  these  are  given  in  Table  XXIII. 

TABLE  XXIII 


WOOD- 

BROWNE'S  SUGAR  ANALYSIS 

MAN'S 

SUGAR 

FOOD 
ANALYSIS 

CONCENTRATION 

MST 

Arabinose 

+  6 

+  104.5 

Dextrose 

+  52.50  -f-  0.018796  p  +  0.00051683  p2 

+    52.5 

p  =  o  to  100  per  cent 

Laevulose 

+  [101.38  —  0.56  /  -f  o.io8(c  —  10)] 

-    92.5 

Invert  sug. 

—  [27.9  —  0.32  /] 

—      20.0 

Lactose 

+  52.53  —0.07  (1  —  20) 

+     52-5 

[/  =  15°  to  25°  C.] 

Galactose 

52.53  =  constant 

+     80.5 

c  =  24  to  40 

Maltose 

140-375  —  0.01837  p  —  0.095  t 

+  138.5 

Sucrose 

+  66.435  +  0.00870  c  —  0.000235  c- 

+    66.5 

0-65  gr.  per  100  cc. 

Xylose 

+    19-0 

Effect  of  Concentration.  —  That  the  specific  rotation  of 
sugar  solutions  is  practically  constant  for  all  concentra- 
tions is  illustrated  in  Table  XXIII.  Biot  (1834)  found  that 
for  aqueous  solutions  of  tartaric  acid  the  specific  rotation 
increases  with  the  dilution.  The  specific  rotation  of  al- 
coholic solutions  of  camphor  decreases  with  the  dilution. 


OPTICAL   ROTATION 


141 


Effect  of  Varying  the  Solvent.  —  The  rotation  of  optically 
active  substances  is  very  different  in  solution  from  the  rota- 
tion of  the  pure  substance,  and  the  nature  of  the  solvent 
has  a  marked  effect  upon  the  magnitude  of  this  rotation. 
Table  XXIV  shows  the  change  in  the  specific  rotation  of 
ethyl  tartrate  and  of  nicotine  when  dissolved  in  different 
solvents,  the  specific  rotation  of  the  pure  substances  being 
respectively  +7.8  and  —161.5. 

TABLE  XXIV 

(Thorp's  Dictionary) 


SOLVENT 

[a]^  Ax  INFINITE  DILUTION 

ETHYL 
TARTRATE 

NICOTINE 

Formanide     *     . 
Water 

+  30-4° 
26.85 

u-5 
9-13 
6.1 
-  19.1 

-    70° 
77-4 
129.4 
140.1 
163.5 
183-5 

Methyl  alcohol  -•"•'• 

Ethyl  alcohol      
Benzene 

Ethylene  bromide                        .     .     , 

The  order  of  rotation  is  the  same  for  these  two  active 
compounds  in  these  various  solvents,  and  Walden  has  found 
this  to  be  true  for  a  number  of  other  substances  and  solvents. 

When  mixed  solvents  are  employed,  various  results  are 
obtained  as  is  illustrated  in  the  case  of  J-tartaric  acid, 
which,  when  dissolved  in  a  mixture  of  acetone  and  ether, 
rotates  the  plane  of  polarization  to  the  left,  while  in  aqueous 
solutions  it  is  dextro-rotatory. 

Muta-rotation.  —  In  the  case  of  freshly  prepared  solutions 
of  certain  substances  the  specific  rotation  undergoes  a  change 
when  the  solution  is  allowed  to  stand,  but  finally  a  constant 
value  is  obtained.  This  change  may  be  either  an  increase 
or  a  decrease.  This  phenomenon  is  known  as  muta-rotation, 
and  is  also  called  birotation,  multirotation,  etc.  This  change 


142  PHYSICAL   CHEMISTRY 

in  the  specific  rotation  is  very  pronounced  in  the  case  of  the 
reducing  sugars,  certain  oxy-salts,  and  lactones.  Dextrose 
gives  a  value  of  105.2  for  freshly  prepared  solutions,  which 
finally  gives  the  constant  value  of  52.5.  This  phenomenon 
is  explained  by  Landolt  and  others  on  the  assumption  of  dif- 
ferent molecular  arrangements  of  active  forms  in  the  freshly 
prepared  solutions  which  gradually  break  down  into  mole- 
cules of  lower  rotation.  This  change  to  a  constant  rotation 
can  be  produced  by  allowing  the  solution  to  stand  for  sev- 
eral hours,  by  boiling  the  solution,  or  by  the  addition  of  a 
small  quantity  of  alkali  or  acid. 

Electromagnetic  Rotatory  Power.  —  Optical  activity  is 
due  to  the  inner  structure,  and  not  many  substances  possess 
this  property.  Electromagnetic  rotatory  power  is  possessed 
by  all  substances.  This  property  was  discovered  by  Fara- 
day in  1846.  He  placed  glass  between  poles  of  a  magnet 
and  found  that  the  plane  of  polarized  light  was  turned.  This 
phenomenon  lasts  only  while  the  current  is  passing. 

The  electromagnetic  rotatory  power  is  a  function  of  the 
temperature,  depends  upon  the  strength  of  the  magnetic 
field,  and,  as  in  the  case  of  optically  active  substances,  is 
dependent  upon  the  density  of  the  solution  and  length  of 
the  observing  tube.  If  polarized  light  which  passes  through 
a  solution  in  the  electric  field  is  reflected  back  through  it, 
the  plane  will  be  turned  back  to  its  original  position  ;  while 
in  case  of  an  optically  active  compound,  if  the  ray  be  sent 
back  through  it,  the  amount  of  rotation  will  be  doubled. 

The  formula  for  the  magnetic  rotation  is  similar  to  that 
for  the  specific  rotation  of  optically  active  substances.  The 
specific  magnetic  rotation  is,  however,  the  ratio  of  the  rota- 
tion of  the  given  substance  to  the  rotation  of  water  which 


Perkin  used  as  the  standard,  i.e.  -  -r-  -^-  =          ,   where 

lp         I0pn 


—•  refers  to  water.     The  molecular  magnetic  rotation  is  the 


OPTICAL  ROTATION 


specific  rotation  multiplied  by  the  molecular  weight  of  the 
substance  divided  by  the  molecular  weight  of  water,  i.e. 

uiQpQm  _  moiecuiar  magnetic  rotation. 
lp<i>o  1 8 

The  molecular  magnetic  rotatory  power  is  an  additive 
as  well  as  a  constitutive  property.  The  value  for  CH2  is 
obtained  from  homologous  series  such  as  the  following: 


CH, 

Paraffins 1.051 

Alcohols 1.057 

Aldehydes        1.022 

Fatty  acids 1.021 

Esters 1.023 


SERIES 

Alkyl  chlorides 
Alkyl  bromides 
Alkyl  iodides 
Phenyl  esters 


I.OI5 
1.031 
1.031 
1-053 


The  individual  values  vary ;  as  in  the  case  of  alkyl  iodide 
they  range  from  1.005  to  1.066.  Perkin  takes  as  the  mean 
value,  CH2  =1.023.  If  there  are  a  number  of  carbon  atoms 
in  the  molecules  of  a  particular  group  of  compounds,  then  by 
deducting  n  times  the  value  of  CH2  from  the  total  magnetic 
rotation,  a  value  is  obtained  which  is  called  the  series  constant 
(5) .  In  the  fatty  acid  series  we  have : 


ACID 

MOLECULAR 
MAGNETIC 
ROTATION 

»Xi.023 

5 

Propionic 

3.462 
4.472 
5.513 
7.552 
8-565 
9-590 

3  X    .023 
4  X    .023 
5  X    .023 
7  X    .023 
8  X    .023 
9  X    .023 
Mean  val 

0-393 
0.380 

0.398 
0.391 
0.381 
0.383 
ue  0.393 

Butyric   
Valeric     
CEnanthylic 

Caprylic            

Pelargonic 

in  which  n  is  the  number  of  carbon  atoms  belonging  to  the 
CH2  group,  and  S  is  the  series  constant  which  is  obtained  by 
subtracting  the  value  of  wCH2  from  the  molecular  magnetic 
rotation.  In  a  similar  manner  the  series  constant  for  a 


144 


PHYSICAL   CHEMISTRY 


large  number  of  series  of  organic  compounds  has  been  worked 
out,  and  in  Table  XXV  a  few  of  these  are  given. 

TABLE  XXV 


SERIES 

FORMULA 

5 

Paraffins  normal 

CnH2 

o  508 

Alcohols,  primary  
Alcohols  iso 

CnH2re+20 
CnHan+20 

0.631 
o  600 

Aldehydes          

CnH2nO 

o  261 

Ketones   .  '  '.     .-  
Fatty  acids 

C»H2nO 

CnH2nO2 

0-375 

O  1QT> 

Unsaturated  acids      .... 
Dibasic  acids     
Formic  esters     
Acetic  esters      

OH»^Qi 

CnH2n_2O4 

CnH2n02 

CnH2nO2 

I-45I 
0.196 

0-495 
O  ^7O 

Ethyl  esters 

CnH2nO2 

O  "^7 

Alkyl  chlorides 

I  988 

Alkyl  bromides       

CreH^+iBr 

3.816 

By  means  of  these  series  constants,  the  value  for  the 
elements  may  be  determined  as  well  as  the  effect  of  the 
linkage  and  the  establishment  of  the  value  of  the  double 
bond.  Having  these  different  values,  and  knowing  the 
molecular  magnetic  rotation,  these  may  be  employed  in 
determining  the  structure  of  organic  compounds.  One 
illustration  of  the  method  will  suffice. 

The  molecular  magnetic  rotation  of  acetoacetic  ester  was 
observed  to  be  6.510,  and  checking  by  this  method  we  have : 

For  acetic  ester  the  series  constant  is 0.370 

For  ketone  the  series  constant  is        .     .     .     .     .     .     .  0.375 

Giving  as  the  mean  of  these  values 0.372 

Since  w  is  6  we  have  6  X  i  .023  =        6.138 

or 6.510 

as  the  calculated  value  which  checks  the  observed  value 
closely  and  indicates  the  ketonic  form  of  the  ester.  Hence 
we  conclude  that  the  structure  of  ace,toacetic  ester  is  ketonic. 


CHAPTER  XIV 
SOLUTIONS 

IT  is  a  familiar  fact  that  the  physical  form  in  which  matter 
exists  is  dependent  on  temperature  and  pressure.  Water 
exists  in  three  physical  forms  which  can  be  changed  one  into 
the  other  by  slight  variations  in  the  temperature  without 
changing  the  pressure.  This  is  true  of  a  very  large  number 
of  substances  ;  but  in  many  cases,  these  changes  in  form  can 
be  much  more  easily  accomplished  by  changing  the  pres- 
sure also,  whereas  some  substances  which  exist  ordinarily 
in  the  gaseous  form  cannot  be  changed  to  the  other  forms 
unless  there  is  a  change  in  the  pressure  as  well  as  in  the 
temperature.  Theoretically  matter  exists  in  all  three  forms, 
—  solid,  liquid,  and  gaseous  —  and  to  these  forms  of  matter 
we  are  to  apply  the  term  phase,  a  concept  which  was  cre^- 
ated  by  Willard  Gibbs  and  which  he  defined  as  follows: 
"  We  may  call  such  bodies  as  differ  in  composition  or  state 
different  phases  of  the  matter  considered,  regarding  all  bodies 
which  differ  only  in  quantity  and  form  as  different  examples 
of  the  same  phase."  This  is  analogous  to  our  conception 
of  form  of  matter,  physical  modification,  or  state.  By  the 
term  phase  we  understand  a  mass  that  is  chemically  and 
physically  homogeneous.  Any  mass  of  matter  under  con- 
sideration which  may  exist  in  one  or  more  phases  is  termed 
a  system. 

The  homogeneity  of  a  system  results  from  the  system 
being  in  a  state  of  equilibrium  which  is  independent  of  the 
time.  For  in  heterogeneous  (non-homogeneous)  systems, 
such  as  a  salt  in  contact  with  a  solvent,  or  two  gases  that 

145 


'•• 

146  PHYSICAL   CHEMISTRY 

have  just  been  brought  into  contact,  the  concentration  is 
different  at  different  places,  and  the  mixtures  are  of  different 
composition  in  different  parts  of  the  systems.  The  systems 
not  being  in  equilibrium  will  change  simultaneously  into 
homogeneous  systems,  and  equilibrium  will  result.  This 
would  also  take  place  if  different  parts  of  the  same  system 
were  at  different  pressures  or  different  temperatures.  Hence, 
our  considerations  are  limited  to  the  state  of  equilibrium  of 
bodies  or  systems  of  bodies  and  consequently  to  homo- 
geneous systems.  The  existence  of  water  in  contact  with 
water  vapor  might  be  considered  contradictory  to  the  idea 
of  physical  homogeneity,  yet  when  the  system  is  of  uniform 
temperature  and  pressure,  equilibrium  exists,  although  we 
have  it  consisting  of  more  than  one  homogeneous  body,  for 
the  water  is  itself  homogeneous  and  the  water  vapor  too. 
In  such  systems  we  must  have  the  same  temperature  and 
the  same  pressure  throughout,  for  otherwise  there  would 
not  be  equilibrium  and  consequently  a  change  would  occur 
in  the  volume  energy  of  the  bodies  that  constitute  the  sys- 
tem. Such  a  system  is  said  to  be  a  one-component  system 
because  it  consists  of  only  one  chemical  individual,  species, 
or  compound. 

Now  this  system  —  water  and  water  vapor  —  consists  of 
two  phases,  the  liquid  and  the  vapor.  It  is  not  necessary 
that  a  phase  consist  of  only  one  body,  for  it  may  be  dis- 
tributed among  a  large  number ;  or,  in  other  words,  a  very 
large  number  of  bodies  of  one  particular  chemical  individu- 
ality may  constitute  a  phase,  as  the  vast  number  of  globules 
of  butter  fat  in  milk  all  constitute  one  phase.  Or,  a  large 
number  of  different  chemical  individuals  may  constitute  one 
phase,  as  the  casein  and  milk  sugar  in  the  water  solution 
constitute  the  second  liquid  phase  in  milk.  This  last  case 
is  an  example  of  a  multiple  component  system.  This  then 
would  give  a  two -phase  system  for  milk.  If  to  distilled 
water  sodium  chloride  is  added,  we  obtain  a  solution  which 


SOLUTIONS  147 

is  physically  as  well  as  chemically  homogeneous  and  there- 
fore constitutes  one  phase.  If  we  continue  to  add  salt,  we 
reach  a  point  beyond  which  no  more  salt  will  go  into  solu- 
tion and  the  solid  added  will  remain  undissolved  and  be 
eventually  in  equilibrium  with  the  solution.  We  now  have 
an  additional  phase  —  one  solid  phase ;  but  if  we  were  to 
decrease  the;,  temperature  of  the  system  sufficiently,  there 
would  appear  solid  water  (ice)  as  a  second  solid  phase,  and 
we  should  have  with  the  vapor  above  the  solution  a  four- 
phase  system.  It  is  possible  to  make  our  selection  such  that 
the  solid  substance  used  is  capable  of  existing  in  two  solid 
modifications,  and  with  the  appropriate  solvent  we  could 
then  have  five  phases :  two  solid  phases  of  the  dissolved 
substance,  the  solid  phase  of  the  solvent,  the  liquid  phase 
(solution),  and  the  vapor  phase  of  the  pure  solvent.  If  we 
select  two  non-miscible  substances,  we  should  then  have 
two  liquid  phases  ;  the  vapor  phase,  and,  if  the  temperature 
is  very  low,  possibly  a  solid  phase.  So  by  the  judicious  selec- 
tion of  substances  we  can  make  any  complexity  of  phases 
we  desire. 

Components.  —  As  in  the  case  of  physical  homogeneity, 
so  also  with  chemical  homogeneity,  it  is  necessary  that  the 
system  be  in  a  state  of  equilibrium,  otherwise  there  may  be 
a  gradual  transformation  of  one  of  the  chemical  individuals 
into  the  other,  or  vice  versa,  and  it  is  not  with  the  process 
of  change  that  we  have  to  do,  but  with  the  state  of  equilib- 
rium to  which  the  subsequent  considerations  apply.  The 
determination  of  the  number  of  components  that  constitute 
a  system  is  not  always  an  easy  matter,  hence  it  is  necessary 
that  the  idea  of  components  be  clearly  in  mind.  In  the 
water  system  consisting  of  the  three  phases,  —  solid,  liquid, 
and  vapor,  —  an  analysis  of  all  the  phases  would  show  that 
they  are  composed  of  oxygen  and  hydrogen  and  that  the 
proportion  is  the  same  in  all  three  phases,  and  further,  that 
this  proportion  is  that  in  which  oxygen  and  hydrogen  com- 


148  PHYSICAL  CHEMISTRY 

bine  to  form  water.  The  system  is  said  to  consist  of  one 
chemical  individual  or  substance  and  consequently  is  desig- 
nated a  one-component  system.  The  same  is  true  of  sulphur ; 
there  would  be  four  phases,  but  all  of  them  would  show  the 
same  composition  by  analysis.  In  the  case  of  water,  how- 
ever, if  the  temperature  was  raised  very  high,  it  would  be 
found  that  the  water  was  decomposed  into  its  constituents, 
hydrogen  and  oxygen,  arid  that  they  existed  as  the  elemental 
substances  in  equilibrium  with  water  vapor.  Here  we 
should  have  a  somewhat  different  state,  as  they  would  then 
be  considered  as  components,  because  they  take  part  in  the 
equilibrium.  Hence,  a  change  in  the  conditions  of  the 
system  may  necessitate  a  change  in  the  number  of  com- 
ponents. We  therefore  distinguish  the  components  of  a 
phase  or  system  as  the  constituents  of  independently  variable 
concentration,  and  they  may  be  either  elements  or  compounds. 
Therefore  we  define  the  components  or  "  individuals  of 
any  reacting  system  as  the  separate  chemical  substances 
undecomposed  in  the  reactions  concerned,  which  are  neces- 
sary to  construct  the  system.  The  number  of  such  (com- 
ponents or)  individuals  to  be  chosen  is  the  smallest  number 
necessary  to  construct  the  system."  (Richards.) 

This  may  be  illustrated  by  the  system  CaCO3  ^  CaO  +  CO2, 
wherein  only  two  of  the  three  constituents,  CaO  and  CO2, 
are  "  undecomposed  in  the  reaction  concerned."  Conse- 
quently the  system  is  a  two-component  system. 

The  composition  of  Glauber  salt  is  Na2SO4  •  ioH2O,  that  of 
its  solution  Na2SO4  and  H2O,  and  that  of  the  vapor  of  the 
solution  is  H20,  so  that,  varying  the  ratios  of  Na2SO4  and 
H2O,  the  constituents  of  the  solution,  we  can  produce  all  of 
the  three  phases,  therefore  this  is  a  two-component  system. 
Similarly  other  hydrates  can  be  obtained  by  variation  of  two 
components.  This  is  also  true  for  double  salts,  such  as 
K2SO4  •  MgSO4  •  3H2O  (Schonite),  K2SO4  •  CuSO4  •  6H2O,  etc., 
where  the  components  are  the  undecomposed  single  salts 


SOLUTIONS  149 

and  water,  therefore  a  three-component  system,  such  as  they 
are,  is  sufficient  to  form  all  modifications  that  can  exist. 

Separation  of  Phases.  —  The  tests  employed  by  the  or- 
ganic chemist  for  the  identification  and  purity  of  substances 
are  by  means  of  phase  transformations  with  a  record  of  the 
accompanying  heat  change.  If  he  desires  to  determine  the 
purity  of  a  beautiful  crystalline  product,  he  determines  its 
so-called  melting  point.  This  .consists  in  nothing  more 
than  determining  at  a  constant  pressure  at  what  temper- 
ature the  solid  and  liquid  phases  are  in  equilibrium.  On 
the  other  hand,  if  the  substance  is  a  liquid,  he  determines 
at  constant  pressure  the  temperature  at  which  the  liquid 
and  vapor  phases  are  in  equilibrium,  that  is,  the  boiling 
point.  If  either  is  constant,  the  substance  has  the  same 
composition  in  both  phases,  and  he  is  working  with  a  one- 
component  system  and  concludes  that  the  substance  is  pure. 
(This  is  true  except  in  some  special  cases  that  will  be  con- 
sidered in  detail  subsequently.)  Not  only  in  the  preparation 
and  identification  of  substances  do  we  make  use  of  the 
phase  conceptions,  but  in  the  preparation  and  purification 
of  the  same. 

Our  gravimetric  methods  are  based  on  the  separation  of 
the  pure  solid  phase  which  is  one  of  the  components  of  our 
multiple  component  system.  In  fractional  crystallization 
we  have  the  separation  of  a  solid  phase,  while  in  the  process 
of  fractional  distillation  we  make  use  of  the  vapor  phase  for 
the  separation  of 'components.  So  in  a  large  majority  of  our 
chemical  manipulations  we  have  to  do  with  the  separation 
of  phases.  When  these  phases  are  alike,  both  solid,  both 
liquid,  or  both  vapors,  the  operation  becomes  much  more 
difficult  and  particularly  is  this  true  in  the  separation  of 
vapor  phases.  In  the  separation  of  these  latter  we  have 
not  as  yet  made  very  rapid  progress. 

When  the  components  are  increased,  the  complexity  of 
some  of  the  systems  is  very  much  increased,  for  there  are 


150  PHYSICAL   CHEMISTRY 

a  great  many  possibilities  in  multiple  component  systems. 
These  compounds  may  be  so  selected  that  they  form  a  phase 
which  conforms  to  the  laws  of  Definite  and  Multiple  Pro- 
portions. Then  the  phase  is  known  as  a  chemical  compound. 
If,  however,  the  components  do  not  conform  to  this  law,  the 
phase  is  called  a  solution.  A  solution  may  better  be  de- 
fined as  a  phase  in  which  the  relative  quantities  of  the 
components  can  vary  continuously  within  certain  limits, 
or  as  a  phase  of  continuously  varying  concentrations. 
There  is,  however,  no  stipulation  as  to  the  particular  phase 
of  which  a  solution  may  be  formed,  therefore  it  is  possible 
that  a  solution  may  be  of  any  of  the  three  phases  —  solid, 
vapor,  or  liquid. 

In  the  case  of  solutions  that  are  in  the  form  of  liquids,  one 
of  the  components  is  called  the  solvent  and  the  other  the  dis- 
solved substance  or  solute.  We  are  familiar  with  many 
examples  of  solutions  wherein  the  solvent  is  liquid  and  the 
dissolved  substance  is  a  solid,  a  liquid,  or  a  vapor  (or  gas). 
Where  solids  act  as  the  solvent  and  the  so-called  solid  solu- 
tions result,  we  have  a  conception  which  is  perhaps  not 
quite  so  well  known  but  which  is  very  common.  Examples 
of  solid  solutions  include  such  double  salts  as  potassium 
and  ammonium  alum,  ammonium  and  ferric  chlorides,  po- 
tassium and  thallium  chlorates,  etc. ;  the  occlusion  of  gases 
by  metals,  such  as  hydrogen  by  palladium  ;  and  the  absorp- 
tion of  oxygen  and  carbon  dioxide  by  glass  at  a  temperature 
of  200°  under  200  atmospheres  pressure.  Copper  diffuses 
into  platinum  and  into  zinc.  For  the  same  reason  hot 
platinum  crucibles  should  not  be  handled  with  brass  tongs. 
Another  very  interesting  case  is  the  passage  of  sodium 
through  sodium  glass  without  any  visible  change.  If 
electrodes  of  lithium  amalgam  are  used,  the  sodium  is  re- 
placed by  lithium  and  the  glass  becomes  opaque  and  crumbly, 
owing  to  the  fact  that  there  was  a  contraction.  It  has, 
however,  been  found  impossible  to  electrolyze  a  sodium  glass 


SOLUTIONS  151 

between  electrodes  of  potassium  amalgam.     Many  other  ex- 
amples of  solid  solutions  will  be  met  in  the  course  of  our  work. 

GAS  AS  SOLVENT 

When  hydrogen  is  introduced  into  a  vessel  containing 
oxygen  at  ordinary  temperature,  after  a  short  time  the 
two  gases  will  be  mixed  thoroughly.  It  is  immaterial  what 
relative  quantities  of  the  two  are  brought  together,  there 
will  be  produced  a  homogeneous  mixture  of  the  two.  This 
is  true  of  any  other  gases  that  do  not  react  chemically. 
So  it  may  be  stated  that  gases  are  miscible  in  all  proportions. 
Here  we  have  a  simple  intermingling  of  the  gases,  and  as  a 
result  we  should  expect  the  properties  of  the  mixtures  to 
be  the  summation  of  those  of  the  individual  constituents, 
and  in  fact  this  is  the  case,  each  individual  gas  conducting 
itself  as  though  the  other  were  not  present.  The  pressure 
of  the  gas  mixture  is  the  sum  of  the  individual  pressures. 
The  specific  heat,  the  power  of  absorbing  and  refracting  light, 
the  solubility,  in  fact  all  of  the  physical  properties  of  the 
gases  remain  the  same  when  they  are  mixed. 

Dewar  has  shown  that  a  vessel  containing  air  is  more 
highly  colored  by  iodine  than  when  the  iodine  is  introduced 
into  one  from  which  the  air  was  removed.  This  is  also  true 
of  a  number  of  gases,  thus  showing  that  the  gas  present 
exerts  a  solvent  action  on  the  iodine  and  more  of  it  is  there- 
fore present.  Villard  (1895)  nas  shown  that  iodine  is  dis.- 
solved  by  CO2,  as  the  spectra  of  the  vapor  do  not  show 
the  least  characteristic  of  gaseous  iodine.  That  iodine  and 
bromine  are  soluble  in  CS2  above  its  critical  temperature, 
and  that  KI  is  soluble  in  alcohol  vapor,  have  been  fully 
demonstrated  by  Pictet,  Wood,  Hannay,  and  Hogarth,  and 
others.  While  the  question  of  a  gas  acting  as  a  solvent  has 
been  quite  fully  demonstrated  in  cases  where  the  solute 
is  a  gas,  liquid,  or  solid,  the  subject  does  not  present  any- 
thing of  importance  in  our  present  consideration  further 


152  PHYSICAL  CHEMISTRY 

than  the  fact  that  a  gas  may  be  considered  as  a  solvent,  thus 
illustrating  our  second  group  of  solvents. 

LIQUID  AS  SOLVENT 

Gas  as  Solute.  —  When  a  gas  is  brought  into  contact 
with  any  selected  liquid,  the  gas  is  absorbed  by  it ;  but  the 
quantity  absorbed  varies  greatly  with  the  liquid  employed, 
with  the  gas  used,  as  well  as  with  the  temperature  and 
pressure.  In  the  case  of  oxygen,  hydrogen,  nitrogen,  and 
many  other  gases,  the  quantity  of  the  gas  dissolved  is  very 
small  whatever  the  liquid  employed.  In  any  case  when  the 
maximum  amount  has  been  absorbed  under  the  prevailing 
conditions,  there  results  a  state  of  affairs  such  that  the  same 
number  of  molecules  of  the  gas  pass  into  the  liquid  and 
pass  from  the  liquid  into  the  gaseous  space  above,  in  unit 
time.  The  system  consisting  of  the  gas  and  the  liquid  is 
said  to  be  in  a  state  of  equilibrium. 

It  was  shown  by  Henry  (1803)  that  the  mass  of  any  gas 
that  dissolves  in  a  selected  solvent  is  in  direct  ratio  to  the 
pressure  of  the  gas.  For  example,  at  three  atmospheres  pres- 
sure three  times  as  much  can  be  dissolved  by  a  liquid  at  a  con- 
stant temperature  as  is  dissolved  at  one  atmosphere  pressure. 
This  law  of  Henry  may  be  expressed  in  a  number  of  ways. 

Statement  of  Henry's  Law.  —  i.  If  we  designate  the 
mass  of  the  gas  in  unit  volume  of  the  liquid  as  the  concen- 
tration of  the  gas  in  the  liquid,  Ct,  and  represent  the  concen- 
tration of  the  gas  in  the  space  above  the  liquid  by  Cv,  then 

the  ratio  of  these  two  concentrations  remains  constant  for 

£ 
all  values  of  the  pressure,  i.e.  —  =k. 

C9 

2.  The  total  quantity  of  a  gas  absorbed  is  always  pro- 
portional to  the  pressure  on  the  gas.  As  we  usually  express 
the  quantity  as  the  mass  (i.e.  the  weight)  then  the  mass  of 
the  gas  per  unit  volume,  i.e.  the  concentration  (Ci)  is  pro- 
portional to  the  pressure.  We  then  have  Ct  =  k'p. 


SOLUTIONS 


153 


3.  If  the  quantity  be  expressed  in  terms  of  volume,  then 
it  follows  from  Boyle's  Law  that  twice  the  mass  occupies 
the  same  volume  under  twice  the  pressure,  and  as  Henry 's" 
Law  states  that  the  quantity  of  gas  absorbed  is  propor- 
tional to  the  pressure,  it  follows  that  the  same  volume  of  gas 
is  dissolved  in  a  specified  quantity  of  a  liquid  at  all  pressures. 

Confirmation  of  Henry's  Law.  —  Henry's  Law  has  been 
subsequently  confirmed  by  a  number  of  workers,  particu- 
larly by  Bunsen  and  by  Khanikof  and  Luginin,  the  results 
of  whose  experiments  on  the  solubility  of  CO2  in  water  are 
given  in  Table  XXVI. 

TABLE  XXVI 


p 

Q 

-f 

P 

Q 

k^ 
P 

69.8 

0.9441 

0.01352 

218.9 

3-1764 

0.01451 

80.9 

I.I6I9 

O.OI436 

236.9 

34857 

0.01472 

128.9 

1.8647 

0.01447 

255-4 

37152 

0.01455 

147.0 

2.1623 

O.OI47I 

273.8 

4.0031 

0.01463 

200.2 

2.9076 

O.OI45I 

3II.O 

4.5006 

0.01447 

It  is  apparent  that  the  value  for  k  is  a  constant  and  that 
the  ratio  of  C, :  p  is  independent  of  the  pressure.  In  other 
solvents  this  law  has  been  shown  to  hold  for  nearly  all  of 
the  gases  that  have  been  studied,  which  include  N2,  H2, 
02,  C02,  CO,  N20,  CH4,  H2S,  NO,  C^o,  C^,  C,R6. 

Exceptions  to  Henry's  Law.  —  In  the  case  of  a  number  of 
gases,  the  amount  of  the  gas  absorbed  has  no  relation  what- 
ever to  the  pressure.  For  example,  HC1,  NH3,  SO2,  HI,  etc., 
are  very  soluble  in  water,  and  their  properties  in  solution 
are  different  from  those  in  the  gaseous  state.  There  appears 
to  be  a  reaction  between  the  solvent  and  solute,  for  in  the 
case  of  HC1  and  water  at  atmospheric  pressure,  a  mixture  of 
a  definite  composition  distills  over  at  106°,  and  in  the  case 
of  HBr  and  H2O,  a  mixture  of  definite  composition  comes 


154 


PHYSICAL   CHEMISTRY 


over  at  126°.     These  gaseous  substances  which  are  so  very 
readily  soluble  in  water  do  not  follow  Henry's  Law. 

Coefficient  of  Absorption  is  defined  as  the  number  of  cubic 
centimeters  of  the  gas  absorbed  by  one  cubic  centimeter  of 
the  liquid  at  o°  C.  and  760  mm.  pressure.  This  coefficient 
for  the  so-called  permanent  gases  is  very  small  and  varies 
from  o.o i  to  0.05,  while  in  the  case  of  those  gases  which  are 
exceptions  to  Henry's  Law  the  coefficient  is  much  larger. 
The  solubility  of  gases  decreases  with  an  increase  of  tem- 
perature, as  is  illustrated  in  Table  XXVII. 

TABLE  XXVII  —  COEFFICIENT  OF  ABSORPTION 


GAS 

o* 

10° 

20° 

30° 

50° 

100° 

Oxygen    .... 

0.04890 

0.03802 

0.03102 

0.02608 

0.02090 

0.01700 

Hydrogen     .     .     . 

0.02148 

0.01955 

O.OI8I9 

0.01699 

0.01608 

0.0160 

Nitrogen 

0.02348 

0.01857 

0.01542 

0.01340 

0.01087 

0.00947 

Carbon  dioxide 

1.713 

1.194 

0.878 

0.665 

0.436 

Ammonia     .     .     . 

1305.0 

915-5 

7154 

Hydrochloric   acid 

506.9 

474-3 

442-3 

411.8 

361.9 

Sulphur  dioxide     . 

79.789 

56.647 

39-374 

27.161 

When  the  temperature  is  raised,  the  gas  can  be  entirely 
removed  from  the  liquid,  except  in  some  cases  in  which  the 
solubility  does  not  conform  to  Henry's  Law.  The  removal 
of  the  gas  can  also  be  accomplished  by  diminishing  the 
pressure.  A  solution  of  sodium  bicarbonate  under  greatly 
reduced  pressure  loses  one  half  of  its  carbon  dioxide.  By 
diminishing  the  pressure  the  blood  loses  the  carbon  dioxide 
and  oxygen  dissolved  in  it. 

Dalton's  Law.  —  When  two  different  gases  are  mixed,  if 
there  is  no  chemical  reaction  between  the  gaseous  particles, 
it  has  been  found  that  each  gas  conducts  itself  as  though  the 
other  gas  was  not  present.  In  fact,  all  of  the  physical  prop- 
erties, such  as  the  pressure  exerted  on  the  walls  of  the 


SOLUTIONS  155 

containing  vessel,  the  specific  heat,  etc.,  experience  no  change. 
Hence,  if  we  have  a  mixture  of  gases  in  contact  with  a  liquid, 
each  individual  gaseous  species  exerts  its  own  individual 
pressure,  and  according  to  Henry's  Law  the  amount  of  this 
particular  gas  absorbed  should  be  proportional  to  this 
pressure.  In  fact,  it  has  been  shown  by  Dalton  (1807) 
that  the  solubility  of  a  gas  is  unaffected  by  the  presence  of 
other  gases  and  that  the  amount  of  each  absorbed  is  pro- 
portional to  its  own  partial  pressure.  This  is  known  as 
the  Absorption  Law  of  Dalton.  By  the  partial  pressure  of 
a  gas  we  mean  the  pressure  exerted  by  that  particular  gas. 
For  example,  if  we  have  a  mixture  of  two  gases,  oxygen  and 
nitrogen,  the  total  pressure,  p,  which  would  be  required  to 
keep  them  at  a  certain  volume  would  be  the  pressure  of  one 
atmosphere.  Now  the  oxygen  in  this  volume  would  exert  its 
own  pressure,  po,  and  the  nitrogen  its  own  pressure,  pNt 
the  sum  of  which  would  equal  the  total  atmospheric  pres- 
sure exerted  upon  the  mixture,  i.e.  p  =  po  +  py,  which 
is  the  expression  for  Dalton 's  Law  that  the  total  pressure 
is  equal  to  the  sum  of  the  partial  pressures  of  the  individual 
species  of  a  gaseous  mixture. 

Water  exposed  to  air  becomes  saturated  at  the  given 
temperature  and  pressure.  Let  us  assume  that  the  pres- 
sure is  760  mm.  This  is  the  total  pressure,  and  since  the 
oxygen  constitutes  20.9  and  the  nitrogen  79.1  per  cent  by 
volume  of  the  air,  then  the  partial  pressure  of  the  oxygen 

will  be  20'9  of  760  mm.,  or  158.84  mm.,  and  that  of  nitrogen 
100.0 


will  be   '9>I  of  760  mm.,  or  601.16  mm.   At  18°  the  solubility 
100.0 

of  oxygen  is  0.0324  and  of  nitrogen  is  0.01605  under  760  mm. 

1^8.84.      -  ••*     ,  ,,   601.16  v 

-* — -X 0.03242  =  0.006776;  X  0.01605  =  0.01269. 

760  760 

0.006776  :  0.01269  : :  34-8  :  65.2  per  cent  of  oxygen  and  of 
nitrogen  respectively. 


CHAPTER  XV 
SOLUTION   OF  LIQUIDS  IN  LIQUIDS— I 

SOLUBILITY 

WHEN  liquids  mix  in  all  proportions  they  are  termed  con- 
sulate liquids.  Water  and  alcohol  are  miscible  in  all  pro- 
portions. They  are  termed  a  pair  of  consulate  liquids. 
Mercury  and  water  do  not  mix  in  any  proportion,  neither  do 
kerosene  and  water.  These  are  non-miscible  liquids.  In- 
termediate between  these  two  types  of  pairs  of  liquids  we 
have  a  very  large  number  of  liquids  which  manifest  a  partial 
solubility  of  the  one  in  the  other.  These  pairs  of  liquids 
are  termed  partially  miscible  liquids. 

If  we  add  ether  to  water,  there  is  formed  a  solution  of  ether 
in  water,  and  this  becomes  more  and  more  concentrated  as 
ether  is  added.  Finally  a  concentration  is  reached  in  which 
a  second  liquid  layer  appears.  We  have  saturated  the  water 
with  ether ;  we  have  two  liquid  layers  that  are  non-miscible. 
If  we  were  to  add  water  to  ether,  the  same  result  would  be 
obtained,  —  the  formation  of  two  non-miscible  layers.  If 
we  continue  to  add  ether  in  the  first  case,  the  relative  volumes 
of  the  two  layers  would  change,  the  lighter  one  increasing 
in  volume  and  the  lower  one  decreasing  until  finally  it 
would  disappear,  when  we  should  have  water  dissolved  in 
ether.  If  we  were  to  add  water  to  ether,  we  should  have 
practically  the  same  result,  the  water  dissolving,  two  liquid 
layers  formed,  the  volume  of  the  layers  changing  until  one 
(the  lighter  in  this  case)  disappeared  with  the  formation 

156 


SOLUTION  OF  LIQUIDS  IN  LIQUIDS  157 

of  a  homogeneous  solution  of  ether  in  water.     This  may 
be  represented  graphically  by  Fig.  15. 

If  A  =  100  per  cent  of  water  and  B  =  100  per  cent  ether,  then  AB 
will  represent  all  possible  concentrations  of  water  and  ether. 

Let  the  concentration  of  the  liquid  layers 
be  represented  by  the  vertical  axis  A  C.  Ethly EUur 

If  we  start  out  with  pure  water,  at  A ,  and 
add  ether,  the  concentration  of  the  solutions 
would  be  represented  by  the  line  AE.  At 
the  concentration  represented  by  E  the  second 
liquid  layer  would  appear.  The  two  liquid 
layers  would  have  the  concentrations  repre- 
sented by  E  and  E'  respectively,  E'  being 


the  concentration  of  the  upper  layer.  FIG.  15. 

Now  as  more  ether  is  added,  the  concentra- 
tion of  the  two  liquid  layers  when  in  equilibrium  would  remain  constant, 
as  represented  by  the  lines  E'F'  and  EF.  By  the  continued  addition 
of  ether  a  point,  F,  would  finally  be  reached  at  which  the  lower  layer 
would  disappear,  and  we  should  have  a  homogeneous  solution  of  water 
in  ether,  the  concentration  of  which  would  be  represented  by  F'.  As 
the  addition  of  ether  is  continued,  solutions  of  water  in  ether  would  be 
formed,  which  are  represented  by  the  line  F'D.  EF  and  E'F1  rep- 
resent the  two  non-miscible  liquid  layers,  and  since  these  are  in  equilib- 
rium, they  represent  saturated  solutions ;  EF  saturated  with  respect 
to  ether  and  the  lighter  layer  E'F'  saturated  with  respect  to  water. 

Hence  it  is  apparent  that  the  two  non-miscible  liquids 
formed  from  the  partially  miscible  liquids  are  saturated 
solutions,  and  these  saturated  solutions  are  themselves  non- 
miscible  liquids,  so  we  may  consider  the  pair  of  saturated 
solutions  formed  from  partially  miscible  liquids  in  the 
class  of  non-miscible  liquids. 

The  determination  of  the  mutual  solubilities  of  this 
system  at  different  temperatures  would  give  us  the  different 
concentration  in  the  two  layers.  So  a  study  of  the  be- 
havior of  a  pair  of  partially  miscible  liquids  resolves  itself 
into  the  determination  of  the  solubility  at  different  tem- 
peratures. Alexejeff  (1886)  took  a  definite  weight  of  water 


PHYSICAL  CHEMISTRY 


and  of  aniline,  put  them  into  a  tube,  sealed  it,  and  determined 
the  temperature  at  which  the  mixture  became  clear.  He 
did  this  for  a  number  of  concentrations  and  obtained  the 
following  data: 


TEMPERATURE 

1  6° 

55° 

77° 

142° 

156° 

164° 

157° 

68° 

39° 

25° 

8.4° 

Aniline  per 

cent    . 

3-i 

3-8 

5-3 

H 

21 

37 

74 

94 

94-5 

95 

95-4 

Let  us  represent  on  the  horizontal  axis  the  concentration  of  aniline 
and  water  in  Fig.  16  by  the  line  AB,  and  on  the  vertical  axis  the  tem- 
perature, then  A  represents  100  per  cent  of  water  and  B  represents 
100  per  cent  of  aniline,  and  AB  represents  all  possible  concentrations  of 
water  and  aniline.  Plotting  the  above  data  we  obtain  the  curve  DCE. 
The  point  D  represents  the  solubility  of  aniline  in  water  and  E  the 
solubility  of  water  in  aniline  at  o°  C.  It  is  apparent  then  as  the  tempera- 
ture increases  the  solubility  of  aniline  in  water  increases,  and  DC  repre- 
sents this.  Similarly  the  part  of  the  curve  EC  represents  the  increased 
solubility  of  water  in  aniline  with  the  increase  in  temperature. 

Above  the  temperature  represented  by  C  (164°)  aniline  and  water 
are  miscible  in  all  proportions,  i.e.  they  are  consulate  liquids  above 
this  temperature,  which  is  termed  the  critical 

I64.i v  solubility  temperature.     The  area  outside  and 

above  the  curve  represents  those  concentra- 
tions and  temperatures  where  aniline  and 
water  are  mutually  soluble  forming  one  liquid 
layer.  Within  the  solubility  curve  DCE  we 
have  the  concentrations  and  temperatures 
where  two  liquid  layers  are  found.  If  quanti- 
ties of  aniline  and  water  represented  by  any 
FIG.  16.  point  within  this  area,  as  ra,  be  mixed  and  al- 

lowed to  come  to  equilibrium  at  any  tempera- 
ture below  C,  the  mixture  will  separate  into  two  liquid  layers,  the  com- 
position of  the  layers  will  be  represented  by  the  two  points  x  y  on  the 
curve  DCE.  The  point  x  represents  the  upper  water  layer  and  y  the 
lower  aniline  layer,  and  the  relative  quantities  of  the  layers  are  repre- 
sented by  the  distances  xm  and  my  respectively,  i.e.  the  weight  of  the 
layer  x  is  to  the  weight  of  the  layer  y  as  the  length  xm  is  to  the 
length  my. 


A  100* 
Water 


100*  B 
Aniline 


SOLUTION  OF  LIQUIDS  IN  LIQUIDS 


159 


Most  partially  miscible  liquids  become  consulate  at  high 
temperatures,  but  there  are  a  number  of  interesting  excep- 
tions to  this.  A  mixture  of  di-  or  trimethyl  amine  and 
water  separates  into  two  liquid  layers  when  the  temperature 
is  lowered,  the  mutual  solubility  increases,  and  if  the  tem- 
perature be  lowered  sufficiently  the  liquids  become  consu- 
late. This  decrease  in  solubility  with  rise  of  temperature 
has  been  observed  in  many  other  cases,  such  as  butyl  al- 
cohol in  water,  and  also  paraldehyde  in  water. 

In  Fig.  17  we  have  minimum  solubility,  while  with  de- 
crease in  temperature  the  solubility  increases  and  finally 
reaches  a  temperature  below  which  the  liquids  are  consulate. 

Many  ketones  and  lactones  show  a  peculiar  characteristic 
in  that  they  have  a  minimum  solubility  at  an  intermediate 
temperature,  and  the  solubility  increases  with  either  an 
increase  or  a  decrease  of  temperature.  In  Fig.  18  we  have 


ISO" 


100% 
JVator 


FIG.  17. 


100* 
Triethylamine 


100  * 
Water 


100* 

Methylethylketone 


FIG.  i 8. 


represented  the  temperature  of  minimum  solubility,  and 
either  above  or  below  this  temperature  the  solubility  in- 
creases. 

It  is  conceivable  that  the  solubility  curve  may  be  a  closed 
curve  as  these  figures  represent  the  three  different  portions 
of  a  closed  curve.  Recently  Hudson  found  this  to  be  real- 
ized in  the  case  of  nicotine  and  water.  Figure  19  represents 
the  effect  of  temperature  on  the  solubility  of  nicotine  in 
water. 


i6o 


PHYSICAL  CHEMISTRY 


150" 


JOO* 
Water 


1009 
Nicotine 


By  heating  mixtures  of  non-miscible  liquids,  we  saw  that 
above  a  certain  temperature  for  all  concentrations  they 
become  consulate.  If,  however,  we  keep  the  temperature 
constant,  we  can  accomplish  practically  the  same  result  by 
adding  a  liquid  which  is  consulate  with  both  the  components. 
So  if  we  have  three  liquid  components  A,  B,  and  C,  and  if 

Cis  consulate  with  A  and  B,  then 
the  mutual  solubility  of  A  and  B 
is  increased,  and  by  addition  of  a 
sufficient  quantity  of  C  one  liquid 
layer  can  be  produced.  It  is  con- 
ceivable, however,  that  if  C  is 
consulate  with  A,  but  only  par- 
tially miscible  with  B,  the  addi- 
FlG  I9-  tion  of  C  to  a  mixture  of  A  and 

B  would  increase  the  solubility  of  A  but  might  decrease  the 
solubility  of  B.  By  the  proper  selection  of  the  three  com- 
ponents we  could  obtain  combinations  which  would  result 
in  the  formation  of  these  three  classes  of  reactions : 

1.  The  three  components  form  only  one  pair  of  partially 
miscible  liquids. 

2.  The  three  components  form  two  pairs  of  partially  mis- 
cible liquids. 

3.  The  three  components  form  three  pairs  of  partially 
miscible  liquids. 

Triangular  Diagram.  —  In  representing  the  relation  of 
the  mutual  solubility  to  the  change  in  temperature  we  used 
the  horizontal  axis  to  represent  the  concentration  and  the 
vertical  axis  to  represent  the  temperature.  To  represent 
the  concentration  of  three  liquid  components  use  is  made 
of  the  triangular  diagram,  and  since  this  is  on  a  plane  sur- 
face it  represents  the  concentration  at  one  temperature. 
There  are  two  methods  of  representing  the  concentration  by 
means  of  a  triangular  diagram,  and  we  shall  use  the  method 
of  Roozeboom,  and  only  refer  to  that  of  Gibbs  indirectly. 


SOLUTION  OF  LIQUIDS  IN  LIQUIDS 


161 


Construct  an  equilateral  triangle,  A  CB,  Fig.  20.  We  saw  that  a  line 
such  as  AB  would  represent  all  possible  concentrations  of  A  and  B. 
Similarly  let  BC  represent  all  possible  concentrations  of  B  and  C,  and 
AC  represent  all  possible  concentrations  of  A  and  C.  The  concentra- 
tion of  any  mixture  of  A ,  B,  and  C  will  be  represented  by  some  point 
within  the  triangle.  Assume  the  ends  of  the  lines,  i.e.  the  corners  of  the 

100% 


100% 
0 


70  60  50  40  30 

30  40  60  €0  70 

FIG.  20. 


zo          10          o* 

80  90  100 1 


triangle,  to  represent  100  per  cent  respectively  of  A,  B,  and  C;  then 
divide  the  sides  into  10  equal  parts  and  draw  lines  parallel  to  the  sides 
of  the  triangle.  Then  from  the  intersection  of  these  lines  the  composi- 
tion of  a  mixture  represented  by  any  point,  such  as  O,  can  be  readily 
ascertained.  Counting  the  composition  of  A  on  the  lines  parallel  to 
the  side  opposite  A,  we  have  4,  i.e.  40  per  cent;  counting  similarly 
for  B,  we  find  i.o  or  10  per  cent,  and  since  O  is  on  5th  line  from 
the  side  opposite  C,  then  the  concentration  of  C  is  50  per  cent,  and 
that  of  our  mixture  is  A  =40  per  cent,  B  =  10  per  cent,  and  C  =  50 
per  cent. 


162 


PHYSICAL   CHEMISTRY 


Ether  and  alcohol  are  miscible  in  all  proportions  (and  also 
water  and  alcohol),  but  water  and  ether  are  only  partially 
miscible.  So  if  a  mixture  of  ether  and  water  be  taken  in 
known  proportions  of  about  equal  quantities  and  shaken 
with  a  little  alcohol  and  allowed  to  come  to  equilibrium,  two 


FIG.  "2i. 

liquid  layers  will  be  formed.  By  repeating  this  with  suc- 
cessive additions  of  alcohol  a  concentration  will  eventually  be 
reached  at  which  but  one  liquid  layer  is  formed.  If  the 
point  of  concentration  be  established  where  just  one  drop 
of  the  alcohol  will  cause  the  disappearance  of  one  of  the  two 
liquid  layers,  we  have  a  point  of  saturation.  Similarly  suc- 
cessive points  of  saturation  could  be  established  syntheti- 
cally for  all  concentrations  of  ether  and  water.  Then  by 


SOLUTION  OF  LIQUIDS  IN  LIQUIDS  163 

plotting  these  results  on  a  triangular  diagram,  we  would 
have  a  curve  similar  to  x  y  z  y\  %i  in  Fig.  21. 

Let  W  represent  water,  E  ether,  A  alcohol ;  then  the  sides  of  the 
triangle  will  represent  all  possible  mixtures  of  the  three  pairs  of  liquids, 
taken  two  at  a  time.  Since  ether  is  partially  soluble  in  water,  x  repre- 
sents the  saturated  solution  of  ether  in  water,  similarly  Xi  represents  a 
saturated  solution  of  water  in  ether.  The  line  Wx  would  represent  solu- 
tions of  ether  in  water  and  Exi  solutions  of  water  in  ether. 

The  series  of  saturated  solutions  of  water,  ether,  and  alcohol  at  con- 
stant temperature  may  be  represented  schematically  by  the  isotherm 
x  y  z  yi  XL  If  one  starts  with  the  liquid  phase  designated  by  x  and 
varies  the  three  components,  the  line  xyz  would  represent  one  series  of 
saturated  solutions.  From  Xi  the  same  point  z  would  be  reached,  and 
the  curve  Xiyiz  would  represent  the  composition  of  the  other  series  of 
saturated  solutions.  So  by  starting  with  the  concentration  designated 
by  either  x  or  Xi  and  varying  the  composition,  the  same  concentration 
of  saturation  as  represented  by  the  point  z  would  be  reached,  where  the 
two  solution  phases  become  identical.  Hence  the  isotherm  x  y  z  yi  x\ 
represents  the  series  of  saturated  solutions  of  the  three  components 
which  are  in  equilibrium  at  a  definite  constant  temperature. 

Above  and  outside  of  this  isotherm  is  the  field  of  unsaturated  solu- 
tions, and  the  portion  of  the  figure  included  by  the  curve  represents 
the  field  of  mixtures  which  separate  into  two  liquid  phases,  the  compo- 
sition of  which  is  given  by  some  two  points  on  the  isotherm.  Since  the 
isotherm  represents  the  composition  of  these  saturated  solutions  in 
equilibrium,  the  addition  of  the  component  W  or  E  will  cause  clouding. 
Now  let  us  inquire  whether  it  makes  any  difference  which  of  the  con- 
stituents is  added.  We  saw  that  the  location  of  x  was  due  to  the 
saturation  of  W  by  E,  so  any  further  addition  of  W  would  not  cause 
clouding  of  this  solution,  but  as  we  follow  up  the  isotherm  there  must 
come  a  point  at  which  the  addition  of  W  will  cause  clouding.  Such 
a  point,  y,  is  where  the  line  WH  drawn  through  W  is  tangent  to  the 
curve.  The  same  is  true  for  the  addition  of  the  component  E,  the  line 
EK  through  E  being  tangent  to  the  curve  at  yi.  It  has  been  shown  ex- 
perimentally that  if  to  a  mixture  of  A  and  E  containing  more  of  E  than 
indicated  by  H,  W  be  gradually  added,  clouding  will  eventually  take 
place  and  the  mixture  separate  into  two  liquid  phases ;  but  if  W  be 
added  to  a  mixture  of  E  and  A  containing  less  of  E  than  indicated  by  H, 
no  clouding  will  result.  The  same  reasoning  may  be  applied  to  the  addi- 
tion of  E  to  solutions  of  W  and  A  containing  more  or  less  of  W  than  indi- 
cated by  K,  clouding  occurring  in  the  first  case  and  not  in  the  second. 


1 64  PHYSICAL  CHEMISTRY 

It  is  therefore  apparent  that  the  isotherm  is  divided  into  four  parts 
which  correspond  to  the  following  four  distinct  sets  of  equilibria : 

1.  The  solutions  represented  by  the  line  xy  are  saturated  with 
respect  to  E,  and  an  excess  of  W  does  not  produce  a  precipitate. 

2.  The  solutions  represented  by  the  line  yz  are  saturated  with  respect 
to  £,  and  an  excess  of  W  or  E  produces  a  precipitate  of  E. 

3.  The  solutions  represented  by  the  line  zy\  are  saturated  with 
respect  to  W,  and  an  excess  of  W  or  E  produces  a  precipitate  of  W. 

4.  The  solutions  represented  by  the  line  yix\  are  saturated  with 
respect  to  W,  and  an  excess  of  E  does  not  produce  a  precipitate. 

Above  the  solubility  curve  we  have  the  area  of  unsaturated  solutions, 
while  within  the  curve  all  possible  mixtures  of  water  and  ether  and 
alcohol  which  will  separate  into  two  liquid  layers  may  be  represented. 
Any  point,  such  as  d,  represents  the  proportions  of  water,  ether,  and 
alcohol  which  when  shaken  together  and  allowed  to  come  to  equilibrium 
would  separate  into  liquid  layers ;  the  composition  of  the  lower  heavier 
liquid  layer  would  be  represented  by  some  point,  as  m,  on  the  solubility 
curve  and  the  upper  liquid  layer  by  n  on  the  other  side  of  the  solubility 
curve.  The  straight  line  passing  through  the  point  d  and  connecting 
these  two  points  is  designated  the  tie  line.  If  any  other  mixture,  rep- 
resented by  a  point  k  on  this  line,  was  to  be  prepared  and  allowed  to 
come  to  equilibrium,  the  composition  of  the  two  layers  would  also  be 
represented  by  the  same  two  points  m  and  n  on  the  solubility  curve. 
That  is,  if  we  were  to  take  a  number  of  mixtures  represented  by  points 
on  this  tie  line  and  allow  them  to  come  to  equilibrium,  the  upper  layers 
on  analysis  would  all  be  found  to  have  the  same  composition  represented 
by  n,  while  the  lower  layers  would  all  have  the  composition  represented 
by  the  point  m  on  the  solubility  curve. 

Another  case  similar  to  the  water-ether-alcohol  system  is 
that  of  silver,  lead,  and  zinc.  Molten  lead  and  silver  are 
miscible  in  all  proportions,  silver  and  zinc  are  also  consu- 
late, but  lead  and  zinc  are  only  partially  miscible.  This 
system  has  been  worked  out  by  Wright,  who  obtained  the 
data  given  in  Table  XXVIII. 

The  values  given  in  the  horizontal  rows  represent  com- 
position of  upper  and  lower  layers  in  equilibrium  at  the 
particular  temperature.  These  would  compare  to  such 
points  as  n  and  m  in  Fig.  2 1 ,  which  are  designated  conjugate 
points,  and  the  liquids  are  termed  conjugate  liquids.  The 


SOLUTION  OF  LIQUIDS  IN  LIQUIDS 


composition  of  the  upper  layer  is  much  richer  in  silver  than 
is  the  lower  layer.  So  by  this  means  silver  can  be  sep- 
arated from  lead  and  the  upper  layer  rich  in  silver  can  be 

TABLE  XXVIII 


UPPER  LAYER  PERCENTAGE  AMOUNT  or 

LOWER  LAYER  PERCENTAGE  AMOUNT  OF 

Silver 

Lead 

Zinc 

Silver 

Lead 

Zinc 

40.89 

3.38 

55-73 

1-54 

96.28 

2.18 

47.68 

379 

48.53 

2-39 

9578 

1-83 

52.80 

4.09 

43.11 

4.18 

94-43 

1-39 

60.14 

9.00 

30.86 

10.22 

88.02 

1.76 

65.34 

13.67 

20.79 

15.69 

81.88 

2-43 

60.35 

28.42 

11.23 

29-53 

68.03 

2.44 

skimmed  off  from  the  lower  liquid  layer.  This  method 
constitutes  the  Parkes'  Process  for  the  desilverization  of 
lead.  In  fact,  this  process  is  simply  an  example  of  the  dis- 
tribution of  a  substance  between  two  liquid  layers. 

Saturated  solutions  are  non-miscible  and  so  this  is  a  special 
case  of  two  non-miscible  liquids ;  and  if  we  have  a  third 
component  soluble  in  both  the  liquid  components,  this  third 
component  will  be  distributed  between  the  two  liquid 
phases.  We  saw  according  to  Henry's  Law  that  the  ratio 
of  the  concentration  (Cv)  of  a  gas  in  the  gaseous  space  and 

the  concentration  (C/)  in  the  liquid  at  equilibrium  is  always 

£ 
equal  to  a  constant  — -  =  k.     Now  if  we  apply  this  law  to 

LI 

the  distribution  of  a  substance  between  two  liquid  layers, 
then  the  coefficient  of  distribution  is  constant  if  the  molec- 
ular species  are  the  same  in  both  liquids.  For  the  equilib- 
rium between  two  non-miscible  liquids  in  which  the  third 
component  is  dissolved  we  find  that  the  ratio  of  the  concen- 
trations, C\  of  the  third  component  in  the  one  liquid  and 


1 66  PHYSICAL   CHEMISTRY 

the  concentration  Cz  in  the  other  liquid,  is  a  constant,  i.e. 

>5 

-r  =  k.    That  is,  the  ratio  of  distribution  between  two  liquids 
C\ 

is  a  constant.     This  is  known  as  Nernst's  Distribution  Law. 

This  law  has  its  application,  as  we  have  seen,  to  metal- 
lurgical processes,  and  it  is  apparent  that  the  greater  the 
constant  the  more  of  the  dissolved  substance  (Ag,  for  ex- 
ample) can  be  removed  from  the  liquid  by  adding  zinc.  As 
the  solubility  of  silver  is  greater  in  aluminium  than  in  zinc, 
the  substitution  of  aluminium  for  zinc  would  give  a  larger 
value  for  the  constant,  and  consequently  a  greater  quantity 
of  silver  would  be  found  in  the  upper  layer,  and  therefore  a 
greater  percentage  extraction.  So  the  practice  consists  in 
adding  a  considerable  quantity  of  aluminium  to  increase  the 
efficiency  of  the  desilverization  of  the  lead. 

Shaking  Out  Process.  —  The  ordinary  shaking  out  pro- 
cess employed  in  the  organic  laboratory  is  nothing  more 
than  the  application  of  this  principle.  If  a  compound  is 
prepared  in  an  aqueous  solution  and  this  solution  shaken 
with  ether,  in  which  the  substance  is  more  soluble,  and  the 
ether  is  then  removed  by  means  of  a  separatory  funnel  and 
evaporated,  the  separated  material  is  obtained  in  the  free 
state.  The  greater  the  distribution  ratio  the  more  efficient 
the  extraction,  and  it  is  better  to  extract  with  successive 
small  quantities  of  the  solvent  than  to  use  the  total  quan- 
tity at  one  time,  as  the  following  consideration  will  show. 

Let  us  assume  that  we  have'  12  grams  of  a  substance  dis- 
solved in  100  cc.  of  water  and  that  it  is  twice  as  soluble  in 
benzene  as  it  is  in  water.  If  we  add  an  equal  volume  of 
benzene  to  the  100  cc.  of  water,  then  the  substance  dis- 
solved will  distribute  itself  between  the  benzene  and  water 
in  the  ratio  of  2:1,  and  f  of  12,  or  8  grams,  or  66 f  per 
cent,  will  be  contained  in  the  benzene,  and  ^  of  12,  or  4 
grams,  or  33^  per  cent,  will  remain  in  the  water.  Hence, 
by  extracting  with  equal  quantities  of  the  benzene,  66  f 


SOLUTION  OF  LIQUIDS  IN  LIQUIDS  167 

per  cent  of  the  substance  could  be  extracted.  Now  as- 
sume that  we  divide  the  benzene  into  two  portions  of  50  cc. 
each  and  extract  the  100  cc.  of  aqueous  solution  with  them 
successively.  Since  the  substance  is  twice  as  soluble  in 
benzene  as  in  water,  50  cc.  of  benzene  will  dissolve  as  much 
of  the  substance  as  the  100  cc.  of  water,  and  so  after  shaking 
100  cc.  of  water  with  50  cc.  of  benzene  the  substance  would 
be  equally  divided  between  the  two  solvents  or  in  the  ratio 
of  i :  i,  and  one  half  of  the  substance  would  be  extracted, 
i.e.  50  per  cent.  By  extracting  again  with  50  cc.  of  benzene 
it  is  apparent  that  50  per  cent  of  the  remainder  would  be 
extracted,  or  25  per  cent  of  the  original  quantity.  Hence, 
by  extraction  with  100  cc.  of  benzene,  using  successively  50 
cc.  portions,  the  total  amount  of  the  dissolved  substance 
removed  is  75  per  cent  as  against  66  f  per  cent  when  it  was 
all  used  at  once.  It  is  better,  therefore,  to  extract  several 
times  with  small  quantities  of  the  liquid  than  to  extract  once 
with  a  volume  equal  to  the  aggregate  of  the  volumes  used. 


CHAPTER  XVI 

SOLUTION   OF  LIQUIDS   IN   LIQUIDS  —  H 
VAPOR  PRESSURE 

WATER  boils  at  a  lower  temperature  on  a  high  mountain 
than  it  does  in  a  valley.  This  is  commonly  explained  by 
saying  that  the  pressure  exerted  by  the  atmosphere  on  the 
surface  of  the  water  is  less  at  the  higher  altitude,  or  that  the 
liquid  water  passes  into  the  vapor  phase  at  a  lower  tem- 
perature when  the  pressure  is  diminished.  This  fact  is 
made  use  of  in  organic  chemistry  when  we  carry  on  the 
operation  known  as  distillation  under  diminished  pressure. 
At  these  respective  temperatures  under  their  correspond- 
ing pressures  there  exists  a  state  of  equilibrium  between  the 
vapor  and  the  liquid,  and  the  liquid  will  all  pass  over  into 
the  vapor  phase  without  change  in  temperature,  if  heat  be 
continuously  supplied.  If  at  these  various  temperatures  of 
equilibrium  the  corresponding  pressures  be  determined  and 
represented  diagrammatically  so  that  the  ordinates  repre- 
sent the  pressures  and  the  abscissae  the  temperatures,  and 
if  the  points  are  connected  by  a  curve,  we  should  have  the 
values  for  all  intermediate  temperatures  and  pressures. 
Such  a  curve  is  known  as  the  Vaporization  Curve  and  repre- 
sents all  possible  temperatures  and  pressures  at  which  the 
liquid  and  vapor  are  in  stable  equilibrium.  It  can  there- 
fore be  designated  an  Equilibrium  Curve.  The  pressure  that 
the  vapor  exerts  under  these  conditions  of  equilibrium  is 
designated  the  Vapor  Pressure  of  the  substance. 

Methods  of  determining  vapor  pressures  of  substances 
are  usually  classified  as  the  static  method  and  the  Ramsay 

1 68 


SOLUTION  OF  LIQUIDS  IN  LIQUIDS 


169 


and  Young  or  dynamic  method.  By  the  static  method  the 
substance  is  placed  in  a  Torricellian  vacuum  above  a  column 
of  mercury,  is  heated,  and  the  pressure  determined  by 
change  in  height  of  the  column  of  mercury. 

By  the  Ramsay  and  Young  method  the  pressure  is  kept 
constant  and  the  temperature  is  varied  until  equilibrium  at 
that  pressure  is  established. 

We  shall  consider  the  vapor  pressure  determinations  of 
two  substances,  benzene  and  water,  and  represent  them  dia- 
grammatically.  When  the  pressures  are  represented  as 
ordinates  and  the  temperatures  as  abscissae,  the  diagram  is 
known  as  a  p-t  diagram,  that  is,  a  pressure-temperature 
diagram. 

The  following  values  for  benzene  have  been  found  by 
Ramsay  and  Young,  and  subsequently  confirmed  by  Fischer : 

TABLE  XXIX  —  VAPOR  PRESSURE  OF  BENZENE 


t 

p  IN  MM.  HG. 

t 

p  IN  MM.  HG.  , 

/ 

p  IN  MM.  HG. 

0° 

26.54 

5° 

34.80 

40° 

180.20 

I 

28.04 

6 

36.69 

50 

268.30 

2 

29.61 

IQ 

45-19 

60 

388.51 

3 

31.26 

20 

74-13 

70 

548.16 

4 

32.99 

30 

117-45 

80 

755-00 

The  curve,  AB  in  Fig.  22,  represents  the  vapor  pressure  curve  of  liquid 
benzene,  and  is  an  equilibrium  curve,  as  it  represents  the  pressures  and 
the  corresponding  temperatures  at  which  the 
liquid  and  vapor  of  benzene  are  in  equilibrium. 
The  curve  AB  divides  the  area  into  two  parts, 
and  is  then  the  boundary  between  the  area 
above  the  line  representing  the  liquid  phase  and 
that  below  which  represents  the  vapor  phase. 
The  area  between  the  curve  AB  and  the  tem- 
perature axis  represents  the  pressures  and  tem- 
peratures at  which  benzene  exists  as  a  vapor, 
while  the  area  above  and  bounded  by  AB  and  FIG.  22. 


170 


PHYSICAL  CHEMISTRY 


the  pressure  axis  represents  the  pressures  and  temperatures  at  which 
benzene  will  exist  as  a  liquid. 

In  a  like  manner  we  give  values  for  the  vapor  pressure 
of  water : 

TABLE  XXX  —  VAPOR  PRESSURE  OP  WATER 


t 

p  IN  MM.  HO. 

/ 

P  IN  MM.  HO. 

-  10° 

2.144 

120° 

1484 

0 

4-58 

130 

2019 

+  20 

17-54 

150 

3568 

40 

55-34 

20O 

11625 

60 

149.46 

250 

29734 

80 

355-47 

270 

41101 

IOO 

760.0 

364.3 

147904 

(194.6,  atmos- 

pheres C.  P.) 

In  Fig.  23  AB  represents  the  vapor  pressure  curve  for  water  and  is  an 
equilibrium  curve  as  well,  for  it  represents  the  equilibrium  between 
liquid  water  and  vapor  for  all  intermediate 
temperatures.  It  likewise  represents  the 
boundary  between  areas  where  the  liquid  and 
the  vapor  phases  of  water  exist. 

These  two  examples  are  sufficient  to 
illustrate  the  method  of  representing  the 
condition  of  equilibrium  in  a  two-phase 

; liquid- vapor  one-component  system,  and 

FlG"  23'  this   method   is   general  in  its  applica- 

tion. With  a  constant  mass  the  state  of  a  system  is  defined 
by  arbitrarily  fixing  one  of  the  variable  factors.  For  if  the 
temperature  is  fixed,  then  the  pressure  at  which  the  liquid 
and  vapor  coexist  is  also  fixed,  and  is  represented  by  a  point 
on  the  curve  A  B  at  which  a  line  perpendicular  to  the  t  axis 
at  that  particular  value  for  the  temperature  cuts  the  curve 
A  B.  If  we  fix  the  pressure,  the  temperature  at  which  the 
vapor  and  liquid  coexist  is  also  fixed. 


SOLUTION  OF  LIQUIDS   IN  LIQUIDS  171 

The  mass  of  the  phase  or  phases  does  not  influence  the 
equilibrium  of  the  system,  for  if  we  increase  the  pressure,  the 
vapor  phase  will  disappear.  The  pressure  is  independent  of 
the  relative  or  absolute  volumes  of  the  vapor  and  liquid 
phases.  If  the  pressure  and  temperature  are  maintained  con- 
stant, it  does  not  matter  whether  we  have  500  or  50  cc.  of  the 
liquid  present,  the  equilibrium  will  be  preserved  and  we  could 
remove  most  of  the  liquid  without  disturbing  the  equilibrium. 

Limits  of  the  Vapor  Pressure  Curve.  —  It  is  natural  to 
inquire  to  what  pressure  and  temperature  it  is  possible  to 
subject  a  two-phase  liquid- vapor  one-component  system, 
such  as  water  or  benzene,  and  still  obtain  a  condition  of 
equilibrium  between  the  two  phases.  The  vapor  pressure 
curve  is  a  boundary  curve  and  separates  the  area  of  the 
diagram  into  the  areas  of  pure  liquid  and  pure  vapor ;  hence, 
if  we  follow  this  curve  to  a  sufficiently  high  temperature 
with  its  corresponding  pressure,  we  reach  the  point  at 
which  there  is  no  distinction  between  the  liquid  and  the 
vapor  phases,  and  the  system  ceases  to  be  heterogeneous  and 
is  a  homogeneous  single  phase.  This  would  occur  at  the 
temperature  at  which  there  is  no  distinction  between  the 
vapor  and  liquid,  that  is,  at  the  critical  temperature,  and  the 
corresponding  pressure,  called  the  critical  pressure.  Hence, 
the  vapor  pressure  curve  must  end  at  the  critical  point,  and 
above  this  temperature  there  is  no  pressure  great  enough 
to  produce  the  liquid  phase.  In  the  case  of  water  the 
vapor  pressure  curve  would  terminate  at  a  temperature  of 
633°  absolute,  and  a  pressure  of  195.5  atmospheres,  which 
are  called  respectively  the  critical  temperature  and  critical 
pressure  of  water.  For  benzene  the  critical  values  are 
561.5°  absolute  and  47.89  atmospheres  pressure. 

It  is  a  familiar  fact  that  if  the  temperature  of  a  liquid, 
as  water,  is  lowered,  there  occurs  a  time  when  the  substance 
ceases  to  exist  in  the  liquid  phase  and  a  new  phase  appears 
—  the  solid  phase.  Hence,  it  follows  that  there  must  be  a 


172  PHYSICAL   CHEMISTRY 

lower  limit  to  the  vapor  pressure  curve  for  liquid  water, 
that  is,  to  the  vaporization  curve.  It  is  also  a  familiar 
fact  that  when  clothes  are  placed  on  the  line  in  winter, 
they  freeze,  thus  becoming  stiff  and  hard.  Later  they  are  all 
found  to  be  soft  and  dry.  This  is  due  to  the  fact  that  the 
water  on  exposure  to  the  cold  becomes  ice  and  later  disap- 
pears in  the  form  of  vapor.  That  is,  the  solid  water  (ice) 
passes  directly  from  the  solid  to  the  vapor  phase  without 
passing  through  the  intermediate  liquid  phase.  This  happens 
in  the  case  of  a  large  number  of  substances,  for  exam- 
ple, if  mercuric  chloride  is  heated  at  ordinary  atmospheric 
pressure,  it  liquefies,  and  if  the  heat  be  increased,  the  liquid 
passes  into  the  vapor  phase.  If,  however,  the  pressure  is 
diminished  to  200  or  300  mm.  and  heat  applied,  it  is  found 
that  the  solid  passes  over  into  the  vapor  phase  without 
passing  through  the  intermediate  liquid  phase.  This  pas- 
sage of  a  substance  from  the  solid  to  the  vapor  phase  with- 
out passing  through  the  intermediate  liquid  phase  is  desig- 
nated sublimation.  The  solid  like  the  liquid  has  a  certain 
tendency  to  pass  into  the  vapor  phase,  and  as  this  can  be 
measured  as  a  pressure,  we  speak  of  the  vapor  pressure  of 
solids.  This  tendency  to  sublime  can  be  measured  in  a 
manner  somewhat  analogous  to  the  determination  of  the 
vapor  pressure  of  liquids,  and  it  may  be 
represented  on  thep-t  diagram ;  the  curve 
representing  the  vapor  pressure  of  a  solid 
is  an  equilibrium  curve  and  represents 
the  equilibrium  between  the  solid  (ice) 
and  vapor,  and  is  called  the  Sublimation 
Curve. 

FiG^J  In   the  case  of   benzene   the   vapor 

pressures  are  given  in   Table    XXIX. 

Representing  these  data  on  the  p-t  diagram,  Fig.  24,  we  have 

CD,  which  terminates  at  the  melting  point  of  benzene,  that  is, 

where  the  sublimation  curve  intersects  the  vaporization  curve. 


SOLUTION  OF  LIQUIDS  IN  LIQUIDS 


In  the  case  of  water  we  have  the  following  values  for  the 
vapor  pressure  of  ice : 

TABLE  XXXI  —  VAPOR  PRESSURE  OF  ICE 


/ 

p  IN  MM.  OF  MERCURY 

t 

p  IN  MM.  OF  MERCURY 

-50° 

O.O29 

-  8° 

2.322 

-  40 

0.094 

-  6 

2.762 

-30 

0.280 

-4 

3-277 

—  20 

0.770 

—  2 

3-879 

~  15 

1.237 

—   I 

4.215 

—  IO 

1.947 

—  0 

4-579 

Water 

FIG.  25. 


Representing  these  values  on  the  p-t  diagram,  Fig.  25,  we 
have  CD,  which  intersects  the  vaporization  curve  CB  at  C. 
This  is  the  melting  point  of  ice  and  is 
therefore  the  upper  limit  or  termination 
of  the  sublimation  curve,  which  is  an 
equilibrium  curve  between  the  vapor 
and  solid  phases,  thus  dividing  the  area 
represented  by  the  p-t  diagram  into  still 
smaller  divisions. 

In  systems  composed  of  two  miscible 
liquids,  the  vapor  pressure  of  the  one  liquid  phase  is  found 
to  depend  on  its  concentration  and  on  the  temperature.  At 
constant  temperature  the  variation  of 
the  vapor  pressure  with  change  of  con- 
centration may  be  represented  on  a 
p-conc.  diagram,  and  three  different 
types  of  curves  are  found  to  represent 
the  vapor  pressure  of  mixtures  of  dif- 
ferent pairs  of  miscible  liquids. 

Let  us  represent  on  a  pressure-con- 
centration  diagram,  Fig.  26,  the  con- 
centration   of    mixtures    of    two   miscible    liquids    and   by 
A    and   B  the  vapor  pressures   at  a   given   temperature. 


FIG.  26. 


100  % 
B 


PHYSICAL  CHEMISTRY 


If  the  vapor  pressures  of  all  mixtures  of  A  and  B  are  inter- 
mediate between  the  vapor  pressures  of  A  and  B,  then  the 
curve  AB  represents  the  vapor  pressures  of  all  mixtures, 
and  the  total  pressure  is  the  sum  of  the  partial  pressures  of 
the  vapor  of  the  two  components.  The  addition  of  a  second 
component  to  a  solvent  may  affect  the  vapor  pressure  in 
one  of  three  ways :  (i)  it  may  lower  the  vapor  pressure, 
(2)  it  may  raise  the  vapor  pressure,  or  (3)  it  may  not  affect 
it. 

In  the  pressure-concentration  diagram,  Fig.  27,  let  C 
and  D  represent  the  vapor  pressures  of  two  miscible  liquids, 
then  as  we  add  D  to  C  the  vapor  pressure  of  C  is  raised. 
If  we  take  D  as  the  solvent  and  add  C,  the  vapor  pressure 
will  be  raised,  and  if  we  plot  these  results  we  obtain  a  curve 
represented  by  COD  which  indicates  a  maximum  vapor 
pressure  for  some  mixture  of  these  two  miscible  liquids. 


C 
100% 


FIG.  27. 


D 

100% 


FIG.  28. 


In  the  pressure-concentration  diagram,  Fig.  28,  let  E  and 
F  represent  the  vapor  pressures  of  two  miscible  liquids. 
Let  us  assume  that  the  addition  of  the  second  ^component 
diminishes  the  vapor  pressure  of  the  solvent ;  then  by  adding  F 
to  E  the  vapor  pressure  will  be  decreased,  and  similarly  by 
adding  E  to  F  the  vapor  pressure  of  the  mixture  will  be  less 
than  that  of  F.  By  plotting  such  results  we  obtain  the  curve 
EMF,  which  represents  a  minimum  vapor  pressure ;  while 
in  the  first  case,  where  the  vapor  pressures  of  the  mixtures 
were  intermediate  between  the  vapor  pressures  of  the 


SOLUTION  OF  LIQUIDS   IN   LIQUIDS  175 

two  components,  we  have  neither  maximum  nor  minimum 
pressures. 

We  have  already  seen  that  the  vapor  pressure  is  the  pres- 
sure which  is  necessary  to  balance  the  tendency  of  the  sol- 
vent to  pass  into  the  vapor  phase,  and  at  a  given  temperature 
this  tendency  is  much  less  than  it  was  before  the  solute  was 
added.  It  will  be  necessary  to  raise  the  temperature  con- 
siderably to  form  the  amount  of  vapor  sufficient  to  produce 
the  pressure  equivalent  to  the  pressure  of  the  vapor  of  the 
pure  solvent.  Therefore,  the  liquid  with  the  lower  vapor 
pressure  at  a  given  temperature  is  the 
liquid  with  the  higher  boiling  point. 
Representing  the  pairs  of  liquids  A 
and  B  on  a  temperature-concentration 
diagram,  Fig.  29,  we  would  have  the 
boiling  point  of  A  higher  than  that  of 
B,  and  since  the  vapor  pressure  of 


m% 


mixtures  of  the  two  liquids  is  inter-  FlG  2g 

mediate  between  that  of  the  liquids 

themselves,  the  boiling  point  of  their  solutions  is  intermediate 
between  the  boiling  points  of  the  pure  liquids,  as  is  shown  by 
the  line  A  B,  which  represents  the  boiling  points  of  all 
mixtures  of  A  and  B. 

To  produce  the  same  amount  of  vapor  from  solutions  of 
two  miscible  liquids  which  can  have  a  minimum  vapor 
pressure,  requires  a  larger  expenditure  of  energy  in  the  form 
of  heat  than  to  produce  the  same  pressure  from  the  pure 
solvent.  So  if  we  take  different  mixtures  of  two  miscible 
liquids  which  manifest  minimum  vapor  pressures  and  de- 
termine the  boiling  points  and  plot  them  on  a  temperature- 
concentration  diagram,  as  in  Fig.  30,  we  obtain  the  curve 
EMF,  which  shows  that  as  we  add  the  component  F  to 
the  solvent  E  the  boiling  point  is  raised,  and  the  rise  is 
greater  the  greater  the  concentration  within  certain  limits. 
The  same  is  true  if  we  use  F  as  the  solvent,  and  as  we  add 


i76 


PHYSICAL   CHEMISTRY 


E  the  boiling  point  of  the  solutions  increases  with  the  in- 
creased concentration  of  E.  We  obtain  the  curve  EMF 
which  shows  a  maximum  boiling  point  for  mixtures  of  E 


100* 

c 


100* 

/> 


FIG.  30. 


FIG.  31. 


and  F.  Pairs  of  miscible  liquids  which  have  a  minimum 
vapor  pressure  curve  also  have  a  maximum  boiling  point 
curve. 

Similarly  it  may  be  shown,  as  represented  in  Fig.  3 1 ,  that 
two  miscible  liquids  which  have  a  maximum  vapor  pressure 
curve  (Fig.  27)  have  a  minimum  boiling  point  curve,  COD. 

COMPOSITION  OF  THE   VAPOR  PHASE 

The  vapor  phase  under  constant  pressure  and  temper- 
ature will  be  in  equilibrium  with  the  liquid  phase,  and  we 
have  just  seen  that  the  pressure  of  the  vapor  phase  is  due 
to  the  vapor  pressures  of  the  individual  components  of  the 
vapor,  i.e.  p  =  pi  -\-  pz,  which  is  Dal  ton's  Law.  The  con- 
centrations in  a  gas  are  proportional  to  the  partial  pres- 
sures, and  hence  we  could  determine  the  concentration  of 
the  components  in  the  vapor  phase  if  we  knew  the  partial 
pressures.  The  determination  of  the  partial  pressures  is 
difficult,  and  satisfactory  methods  have  not  been  devised. 
But  we  can  determine  the  concentration  by  distilling  over 
fractions,  collecting,  and  analyzing  them. 

Let  us  consider  a  pair  of  liquids  whose  mixtures  have 
boiling  points  intermediate  between  the  boiling  points  of 


SOLUTION  OF  LIQUIDS  IN  LIQUIDS  177 

the  two  components.  In  Fig.  32  let  A  and  B  represent  the 
two  components  and  AyB  represent  the  boiling  points  of  the 
mixtures.  Let  us  consider*  a  mixture  represented  by '  the 
point  p,  the  composition  of  which  is,  say,  80  per  cent  A  and 
20.  per  cent  B.  If  we  heat  this  mixture  and  continue  to 
raise"  its  temperature  until  we  intersect  the  boiling  point 
curve  AB  at  z,  the  liquid  will  boil  at  this  temperature,  /„ 
and  the  vapor  which  passes  off  will  be  richer  in  B  than  in  A. 
The  temperature  of  the.  liquid  in  the  flask  will  rise  and  pass 
along  the  line  zA,  and  the  concentration  of  the  liquid  in  the 
flask  will  approach  the  composition 
of  pure  A.  The  distillate  which 
passes  off  at  z  is  richer  in  B  than 
the  liquid  from  which  it  was  dis- 
tilfed,  and  may  be  represented  by 
some  point  as  x.  If  the  vapor  of 
this  composition  is  condensed  and 
then  heated  to  its  boiling  point,  IT 
it  will  be  found  to  boil  at  the 
temperature  ty.  This  will  boil,  and  the  vapor  will  be 
richer  in  B  than  is  represented  by  the  concentration  y, 
i.e.  some  concentration  such  as  w.  The  vapor  w,  if  con- 
densed, would  be  found  to  have  a  boiling  point  /„,  and  the 
vapor  of  this  would  be  richer  in  B.  By  this, process  of 
redistillation  we  are  obtaining  distillates  successively  richer 
in  B,  and  it  is  apparent  that  if  this  be  continued  a  suf- 
ficient number  of  times  we  approach  B  and  thus  com- 
pletely separate  it  from  A.  From  the  liquid  remaining  in 
the  flask  we  obtain  A  and  from  the  distillates  pure  B,  and 
therefore  can  completely  separate  them  by  this  means,  which 
is  termed  fractional  distillation.  Any  point  on  the  curve 
BwxA  represents  the  composition  of  the  vapor  phase,  i.e. 
of  the  distillates,  at  the  boiling  point  of  the  mixture  from 
which  it  was  obtained.  This  curve  is  called  the  Vapor 
Composition  Curve. 


* 


c 


178  PHYSICAL   CHEMISTRY 

In  Fig.  33,  where  we  have  a  maxiiattm  boiling  point,  the 
vapor  composition  curve  is  represented  by  the  dotted  curve 
CcOdD.  If  we  take  any  mixture  richer  in  D  than  the 
maximum  boiling  mixture,  and  fractionate  it,  the  distillate 
will  be  richer  in  D  than  in  C,  and  the  composition  of  the  liquid 
in  the  flask  becomes  richer  in  C.  For  mixtures  richer  in 
C  than  the  maximum  boiling  mixture,  the  vapor  will  be  richer 
in  C  and  the  composition  of  the 
liquid  remaining  in  the  flask  becomes 
richer  in  D.  For  any  mixture  the 
concentration  of  the  liquid  in  the 
flask  tends  to  become  of  the  concen- 
tration as  represented  by  the  con- 
centration 0,  at  which  the  boiling 


100*. 


•      j     •        j  1          1*1  j          r  •      j 

c  D     point  is  the  highest  or  any  mixtures 

FlG'  33'  of  C  and  D,  and  the  composition 

of  the  vapor  is  the  same  as  that  of  the  distilling  liquid,  i.e. 
we  have  a  constant  boiling  liquid,  and  all  of.  the  liquid 
passes  over  without  change  in  temperature. 

This  phenomenon  is  the  same  as  in  the  case  of  pure  sub- 
stances. The  boiling  point  is  used  as  a  means  of  deter- 
mining whether  a  substance  is  pure.  If  the  boiling  point 
is  constant,  we  conclude  that  the  substance  is  a  pure  one 
and  that  the  composition  of  the  vapor  and  of  the  liquid  are 
the  same.  If  this  criterion  be  applied  to  this  boiling  mix- 
ture, the  conclusion  would  be  that  it  is  a  pure  chemical 
compound.  For  a  long  time  such  mixtures  were  considered 
as  chemical  compounds.  In  the  case  of  pure  substances 
the  composition  of  the  liquid  and  vapor  phases  is  the  same, 
irrespective  of  the  pressure  at  which  the  boiling  point  is 
determined.  If,  however,  these  constant  boiling  mixtures 
of  pairs  of  miscible  liquids  be  determined  at  different  pres- 
sures, vapors  of  different  composition  will  be  obtained. 
This  proves  that  they  are  not  chemical  compounds  but 
mixtures. 


SOLUTION  OF   LIQUIDS   IN  LIQUIDS  179 

In  Fig.  34,  EeMfF  is  the  vapor  composition  curve  of  the 
distillates  from  the  mixtures  of  pairs  of  liquids  with  a  jniai- 
mum  boiling  point.  The  distillates  of  mixtures  whose  boil- 
ing points  are  represented  by  EM  are  richer  in  F  than  the 
mixtures  from  which  they  were  obtained,  and  as  these  dis- 
tillates are  continuously  fractionated  by  distillation  the  com- 
position of  the  distillate  approaches  M.  Similarly,  for  the 
liquids  whose  boiling  points  are  < 
represented  by  MF  the  composition  E 
of  the  distillates  obtained  by  frac- 
tional distillation  approaches  M  as 
the  final  value.  That  is,  the  dis- 
tillates of  all  mixtures  upon  frac- 
tionation  give  as  final  values  the 


composition  represented  by  M,  which     -jr  '"  * 

is   that    mixture    with    the    lowest  FlG>  34' 

boiling  point.  At  this  temperature  the  mixture  of  this 
composition  distills  at  constant  temperature  and  the  vapor 
and  liquid  have  the  same  composition.  What  was  stated 
with  respect  to  the  point  0  of  the  maximum  boiling  liquids 
applies  to  the  point  M  of  the  minimum  boiling  liquids ;  the 
composition  varies  with  the  pressure  and  therefore  they  are 
not  pure  chemical  compounds. 

Mixtures  of  the  type  illustrated  in  Fig.  32  are  not  very 
common.  In  the  case  of  methyl  alcohol-water  and  acetone- 
water  mixtures,  approximate  separation  by  fractional  dis- 
tillation can  be  obtained. 

Mixtures  of  the  type  illustrated  in  Fig.  33  are  repre- 
sented by  a  number  of  solutions  of  acids  in  water  where 
maximum  boiling  points  are  obtained  as  illustrated  in 
Table  XXXII. 

Mixtures  of  the  type  illustrated  in  Fig.  34  are  common,  and 
a  few  of  the  more  common  pairs  of  miscible  liquids  that  have 
a  maximum  vapor  pressure  and  a  minimum  boiling  point 
are  given  in  Table  XXXIII. 


180 


PHYSICAL  CHEMISTRY 
TABLE  XXXII 


TEMPERA- 

PER CENT 

SOLVENT 

BOILING 
POINT 

SOLUTE 

BOILING 
POINT 

TURE  OF 
MAXIMUM 

BY 

WEIGHT 

BOILING 

OF 

POINT 

SOLVENT 

Water.     .     .     . 

100° 

Nitric  acid  .     .     . 

86° 

120.5° 

32. 

Water.     .     .     . 

100. 

Hydrochloric  acid 

-82.9 

1  10. 

79.76 

Water.     .     .     . 

IOO. 

Hydrobromic  acid 

-68.7 

126. 

52.5 

Water.     .     .     . 

IOO. 

Hydriodic  acid     . 

-35-7 

127.0 

43-0 

Water.     .     .     . 

IOO. 

Hydrofluoric  acid 

19.4 

120. 

63- 

Water.     .     .     ._ 

IOO. 

Formic  acid     .     . 

99.9 

I07.I 

23.0 

Perchloric  acid  . 

IIO.O 

Water     .... 

IOO. 

203. 

71.6 

Chloroform  .     . 

61.2 

Acetone 

56.4 

64.7 

80. 

Chloroform  . 

61.2 

Methyl  acetate    . 

56.0 

64-5 

78. 

Propionic  acid  . 

140. 

Pyridine      .     .     . 

117-5 

149. 

TABLE  XXXIII 


SOLVENT 

BOILING 
POINT 

SOLUTE 

BOILING 
POINT 

TEMPERA- 
TURE OF 
MINIMUM 
BOILING 
POINT 

PER  CENT 

OF 

SOLVENT 

BY 

WEIGHT 

Water.     .     .     . 

100° 

Ethyl  alcohol  .     . 

78-3° 

78.15° 

4-43 

Water.     .     .     . 

IOO. 

Isopropyl  alcohol 

82.45 

80.35 

12.10 

Water.     .     .     . 

IOO. 

n  Propyl  alcohol  . 

97-2 

87-7 

28.31 

Butyric  acid 

159. 

Water     .... 

IOO. 

99.2 

20. 

Pyridine  .     .     . 

115- 

Water     .... 

IOO. 

92.5 

59- 

Benzene   .     .     . 

80.2 

Methyl  alcohol    . 

64.7 

58.35 

60. 

Benzene   . 

80.2 

Ethyl  alcohol  .     . 

78.3 

68.25 

67.64 

Tertiary     butyl 

alcohol 

82.55 

Benzene      .     . 

80.2 

73-95 

36.6 

Allyl  alcohol      . 

95-5 

Benzene 

80.2 

76-5 

20.O 

Toluene    .     .     . 

109. 

Allyl  alcohol    .     . 

95-5 

9i-5 

50.0 

Ethyl  alcohol    . 

78-3 

Normal  hexane    . 

68.95 

58.65 

2I.O 

Carbon      tetra- 

chloride 

76.75 

Methyl  alcohol     . 

64.7 

55-7 

794 

Ethyl  iodide      . 

72.9 

Methyl  alcohol    . 

64.7 

55-0 

83- 

Ethyl  alcohol    . 

78. 

Ethyl  iodide    .     . 

72.0 

63.0 

14. 

Acetone    .     .     . 

56.4 

Carbon  bisulphide 

46.2 

39-25 

34-0 

Methyl   acetate 

56.0 

Carbon  bisulphide 

45-6 

39-5 

29.0 

SOLUTION  OF  LIQUIDS   IN  LIQUIDS  181 

FRACTIONAL  DISTILLATION  WITH  STEAM 

In  the  case  of  a  one-component  system  of  a  liquid  and 
vapor,  the  vapor  pressure  of  the  pure  liquid  at  the  boiling 
point  under  atmospheric  pressure  is  equal  to  760  mm.  pres- 
sure. That  is,  the  vapor  exerts  a  pressure  of  this  amount 
against  the  tendency  of  the  liquid  to  vaporize.  In  the  case 
of  two  non-miscible  or  partially  miscible  liquids,  the  vapor 
pressure  of  these  at  the  boiling  point  of  the  mixture  will 
be  the  sum  of  the  partial  vapor  pressures  of  the  two  liquids. 
This  will  be  equal  to  the  external  or  atmospheric  pressure,  if 
boiling  under  atmospheric  pressure.  If  carbon  bisulphide 
boils  at  50°  C.  the  vapor  pressure  at  this  temperature  is 
balanced  by  the  atmospheric  pressure,  and  if  we  have  water 
mixed  with  it  at  this  temperature  the  vapor  pressure  of  the 
water  is  appreciable,  as  p  =  pcs,  +  PH&,  hence  the  vapor 
pressure  of  CSz  does  not  have  to  equal  the  atmospheric 
pressure,  as  the  combined  pressures  of  the  carbon  bisulphide 
and  of  the  water  are  equal  to  the  external  pressure.  It  is, 
therefore,  apparent  that  the  aggregate  pressures  of  the  two 
vapors  will  equal  the  atmospheric  pressure  at  a  temperature 
below  50°,  the  boiling  point  of  the  lower  boiling  liquid. 
That  is,  the  mixture  will  boil  at  a  temperature  below  that  of 
the  lower  boiling  liquid.  The  quantities  of  the  substances 
in  the  vapor  phase  will,  of  course,  depend  upon  the  vapor 
pressure  of  the  substances  at  that  temperature.  This  may 
be  illustrated  by  a  specific  case. 

In  the  distillation  of  nitrobenzene  by  steam  the  mixture 
boils  at  99°  C.  at  a  pressure  of  760  mm.  At  this  temperature 
the  vapor  pressure  of  water  is  733  mm.  and  that  of  the 
nitrobenzene  would  be  the  difference  760  —  733  or  27  mm. 
Since  22.4  liters,  the  gram-molecular  volume,  would  contain 
1 8  grams  of  water  vapor  under  the  standard  conditions, 
an  equal  volume  under  760  mm.  pressure  and  at  o°  would 
contain  123  grams  of  nitrobenzene.  Since  the  volumes 


182  PHYSICAL   CHEMISTRY 

are  indirectly  proportional  to  the  pressures  we  would 
have,  as  the  weights  are  proportional  to  the  pressures, 
1  8  gr.  :  %  gr.  :  :  760  mm.  :  733  mm.  (the  vapor  pressure  of 

water  at  99°  C.).     This  gives  -  —     733     grams   of   water 

760 

which  would  pass  over.     In  a  like  manner  we  find  * 


760 
grams  of  nitrobenzene  in  the  distillate.     These  give  us  the 

ratio  of    I23  X  2?  :  l8  X  733   or  367  :  1466  or   i  :  4  as  the 
760  760 

relative  weights  of  the  distillates.  As  the  water  is  much 
lighter  than  the  nitrobenzene,  the  volume  of  water  is  much 
larger  relatively  to  that  of  the  nitrobenzene  that  passes  over. 
If  the  molecular  weight  of  the  substance  being  distilled 
with  steam  is  not  known,  it  can  be  readily  calculated  by 
measuring  the  volume  of  the  liquids  distilled  over,  and  from 
their  specific  gravities  the  weight  could  be  determined  and 
from  this  ratio  the  value  of  m  in  place  of  the  molecular 
weight  of  nitrobenzene  vapor  could  be  calculated. 


CHAPTER  XVII 
PHASE  RULE 

SINCE  we  know  that  the  existence  of  water  in  the  vapor, 
liquid,  or  solid  phase  depends  upon  the  conditions  of  tem- 
perature and  pressure,  the  limiting  value  for  any  particular 
phase  is  a  question  merely  of  the  relation  of  these  factors. 
In  a  consideration  of  the  subject  of  phases  and  of  the  problems 
of  equilibrium  from  this  point  of  view,  we  practically  take 
into  consideration  the  heat  and  volume  energy  and  leave 
out  of  consideration  the  force  of  gravity,  electrical  strains 
and  stresses,  distortion  of  the  solid  mass,  capillary  tension, 
etc.,  and  thus  confine  ourselves  to  those  systems  wherein 
there  exists  only  uniform  temperature,  pressure,  and  chemical 
potential. 

In  a  system  that  contains  only  one  phase,  unless  we  have 
both  the  pressure  and  temperature  designated,  the  con- 
centration is  not  known.  Both  of  these  factors  are  needed 
to  establish  the  system.  We  know  that  both  of  these  in- 
dependent variables  can  be  changed  within  certain  limits 
and  the  system  still  be  maintained  as  a  one-phase  system. 
Then  the  question  arises  :  What  are  the  limits  to  which  these 
independent  variables  can  be  varied  and  yet  retain  the  system 
as  a  one-phase  system  ?  That  is,  What  are  the  boundaries 
of  any  of  these  different  possible  one-phase  systems  such  as 
water,  and  what  will  happen  to  the  system  when  these  limits 
are  exceeded?  If  the  pressure  and  temperature  are  varied 
in  the  proper  direction,  a  vapor  can  be  made  to  condense  into 
a  liquid,  —  the  greater  the  pressure  the  more  of  the  vapor  will 
disappear  and  the  greater  the  liquid  phase  will  become.  The 

183 


1 84  PHYSICAL   CHEMISTRY 

concentration  of  the  system  has  increased  and  we  have  a 
two-phase  system.  If,  on  the  other  hand,  the  pressure  is 
diminished  and  the  temperature  increased  sufficiently,  it 
may  break  up  and  become  disintegrated  by  the  decomposition 
of  the  components.  So  that  the  boundary  limits  in  all 
directions  are  not  accessible  and  hence  not  easily  established 
experimentally. 

By  decreasing  the  temperature  of  the  two-phase  system  of 
water  —  liquid  and  vapor  —  a  new  phase  appears.  This  is 
the  solid  (ice).  When  this  occurs  we  have  the  system  more 
securely  fixed,  as  it  were,  for  none  of  the  variables  can  now  be 
changed  without  causing  the  disappearance  of  some  of  the 
phases  —  ice,  if  the  temperature  is  increased,  or  liquid,  if 
the  temperature  is  decreased.  Every  phase  of  a  system  has 
its  boundaries  or  limitations  on  all  sides,  that  is,  its  sphere 
of  existence.  These  boundaries  are  represented  by  the  in- 
dependent variables  —  the  temperature,  pressure,  and  con- 
centrations. We  see  then  that  every  system  has  a  certain 
amount  of  freedom  in  the  variation  of  its  variables  in  so  far 
as  the  identity  of  the  system  is  not  destroyed,  and  we  have 
also  seen  that  this  sphere  of  freedom  is  not  necessarily 
bounded  on  all  sides  by  other  phases.  This  "sphere  of 
existence  "  is  spoken  of  as  the  number  of  degrees  of  freedom 
of  the  system  and  is  defined  as  "  the  number  of  the  variable 
factors  —  temperature,  pressure,  and  concentration  of  the 
components  —  which  must  be  arbitrarily  fixed  in  order  that 
the  conditions  of  the  system  may  be  perfectly  defined. "  — 
Findlay's  Phase  Rule,  p.  16. 

A  gas  would  have  two  degrees  of  freedom  because,  in  order 
to  determine  its  concentration,  we  should  have  to  define 
both  the  pressure  and  temperature. 

A  system,  liquid-vapor,  has  one  degree  of  freedom,  while 
a  system,  solid-liquid-vapor,  has  no  degree  of  freedom, 
because  a  change  of  any  of  the  variables  would  cause  one  of 
the  phases  to  disappear  and  the  equilibrium  to  be  disturbed. 


PHASE  RULE  185 

In  speaking  of  the  amount  of  variance  or  variation  of  the 
system,  we  say  that  the  system  is  non variant  (invariant), 
monovariant,  divariant,  multivariant,  etc.,  when  the  number 
of  degrees  of  freedom  is  respectively  zero,  one,  two,  three, 
etc.  This  relation  between  the  number  of  degrees  of  freedom, 
the  number  of  independent  variables,  and  the  number  of 
components  of  the  system  has  been  expressed  by  Gibbs  in  his 
celebrated  Phase  Rule,  which  defines  the  system  completely. 
This  Phase  Rule  may  be  stated  as  follows :  The  number  of 
degrees  of  freedom  of  a  system  is  equal  to  the  number  of  com- 
ponents plus  two,  minus  the  number  of  phases.  This  may  be 
expressed  by  the  following  equation : 

JV  +  2  -  P  =  F 

in  which  N  is  the  number  of  components,  P  the  number  of 
phases,  and  F  the  number  of  degrees  of  freedom,  or  the 
variance  of  the  system. 

The  concept  of  phases  has  been  of  great  importance  in 
aiding  the  classification  and  correlation  of  a  large  number  of 
isolated  facts,  in  the  interpretation  of  new  phenomena,  and 
in  guiding  us  in  the  discovery  of  new  phenomena  and  their 
relations.  In  this  respect  the  Phase  Rule  as  a  system  of 
classification  of  interrelated  phenomena  is  to  chemistry  in 
general  what  the  periodic  law  is  to  inorganic  chemistry.  It 
is  really  a  basis  of  classification  of  the  phenomena  of  chemistry 
rather  than  a  separate  division  of  the  subject. 

Ostwald  goes  even  farther  and  states  that  it  is  possible 
from  the  principles  of  chemical  dynamics  -  (the  theory  of  the 
progress  of  chemical  reaction  and  the  theory  of  chemical 
equilibrium)  to  deduce  all  of  the  stoichiometrical  laws,  the 
laws  of  constant  proportion,  the  laws  of  multiple  proportions, 
and  the  law  of  combining  weights.  Through  this  conception 
of  the  phase  introduced  by  Gibbs  and  amplified  by  himself 
and  Franz  Wald,  Ostwald  proceeds  to  deduce  these  laws  in 
his  Faraday  Lecture  (Jour.  Chem.  Soc.,  85,  506  (1904)). 


0" 

FIG.  35. 


1 86  PHYSICAL   CHEMISTRY 

SYSTEM  OF  WATER 

The  p-t  diagram,  Fig.  35,  represents  the  whole  range  of 
temperatures  and  pressures  of  the  system  water,  and  this 
area  is  divided  into  three  areas  representing  the  ranges  of 
temperature  and  pressure  at  which  water  can  exist  as  vapor, 
as  liquid,  and  as  solid.  Each  of  these  three  systems  consists 
of  one  phase,  hence,  according  to  the  Phase  Rule 
N  +  2  —  P  =  F,  we  have  1  +  2  —  1  =  2;  i.e.  two  degrees 
of  freedom  or  a  Divariant  System.  The 
three  divariant  systems  then  are: 

1.  The  area  DCB-t-axi$  representing 
the  vapor  phase, 

2.  The  area   ECB  representing  the 
liquid  phase, 

3 .  The  area  DCE-p-axis  representing 
the  solid  phase. 

It  is  apparent,  as  in  the  case  of  the  liquid  phase,  that  at  a 
point  such  as  G,  if  the  temperature  be  kept  constant,  there 
are  a  large  number  of  pressures  to  which  the  liquid  can  be 
subjected  without  introducing  a  new  phase  or  causing  the 
liquid  phase  to  disappear.  Likewise,  if  the  pressure  at  G 
be  kept  constant,  there  are  a  large  number  of  temperatures 
at  which  the  liquid  phase  persists,  i.e.  the  liquid  phase  is 
capable  of  existing  at  various  temperatures  at  the  same 
pressure.  This  is  true  of  any  other  phase ;  each  pressure  has 
a  number  of  temperatures  and  each  temperature  a  number 
of  pressures  at  which  the  phase  exists. 

The  boundary  between  the  vapor  area  and  the  liquid  area 
is  represented  by  the  curve  CB,  which  is  the  Vaporization 
Curve  and  represents  the  equilibrium  between  the  liquid  and 
vapor  phases.  Since  we  have  two  phases  in  equilibrium, 
according  to  the  Phase  Rule  we  should  have  1  +  2  —  2  =  1, 
or  a  Monovariant  System.  The  same  is  true  of  the  equilibrium 
curve  between  vapor  and  solid,  represented  by  the  Sublima- 


PHASE  RULE  187 

tion  Curve,  DC,  and  the  equilibrium  between  the  solid  and 
liquid  represented  by  the  Fusion  Curve,  EC.  Hence  we  have 
three  monovariant  systems  represented  by  the  following 
curves : 

1.  CB,  representing  equilibrium  between  the  liquid  and 
vapor  phases, 

2.  CD,  representing  equilibrium  between  the  vapor  and 
solid  phases, 

3.  CE,  representing  equilibrium  between  the  liquid  and 
solid  phases. 

The  three  curves  representing  the  monovariant  systems 
intersect  for  water  at  a  point  known  as  the  triple  point. 
This  point  represents  the  only  temperature  and  pressure  at 
which  the  three  phases  —  solid,  liquid,  and  vapor  —  can 
exist  in  equilibrium ;  for  water  this  is  at  4.6  mm.  pressure  and 
at  +  0.0075°.  According  to  the  Phase  Rule,  since  we  have 
three  phases  present  we  should  have  1-1-2—3  =  0;  i.e. 
the  system  is  a  Nonvariant  System. 

We  have  just  denned  the  boundaries  of  the  various  phases 
when  in  equilibrium,  but  it  is  natural  to  inquire  if  any 
particular  phase  can  exist  under  any  other  conditions  than 
those  represented  by  the  diagram.  It  is  known  that  if 
vapor  is  cooled  very  carefully,  it  can  be  obtained  at  a  tem- 
perature much  below  that  at  which  it  should  condense  and 
become  a  liquid.  In  the  diagram,  Fig.  35,  let  F  represent 
some  temperature  and  pressure  of  the  vapor.  By  cooling 
the  vapor  very  carefully  it  may  be  made  to  follow  the 
conditions  represented  by  the  line  FG,  and  at  G,  in  the  liquid 
area,  the  vapor  phase  still  exists.  That  is,  the  vapor  is 
capable  of  existing  under  other  conditions  than  that  rep- 
resented by  the  area  designated  vapor,  but  under  such 
conditions  the  system  is  said  to  be  in  a  state  of  labile  equilib- 
rium ;  and  if  a  minute  trace  of  the  liquid  phase  be  introduced, 
some  of  the  vapor  will  become  liquid  and  assume  a  condition 
of  stable  equilibrium  with  the  vapor  represented  by  a  point 


1 88  PHYSICAL  CHEMISTRY 

H  on  the  equilibrium  curve  CB.  If  we  continue  to  cool  the 
monovariant  system,  liquid-vapor,  it  is  possible  to  con- 
tinue the  curve  CB  into  the  solid  area  to  A ,  without  the  ap- 
pearance of  the  solid  phase.  That  is,  we  have  undercooled 
the  liquid  below  its  freezing  point.  If,  however,  a  portion 
of  the  solid  phase  is  introduced,  the  liquid  phase  will  dis- 
appear and  the  system  will  become  a  system  composed  of  solid 
and  vapor  in  equilibrium.  We  have  not  been  able  to  obtain 
the  solid  phase  under  such  conditions  that  a  liquid  or  vapor 
exists,  but  a  liquid  can  be  heated  above  the  temperature  at 
which  it  is  in  equilibrium  with  the  vapor  phase  and  be  rep- 
resented in  the  vapor  phase  area.  It  is  claimed  that  water 
has  been  heated  to  about  200°  C.  and  still  remained  in  the 
liquid  phase. 

At  the  triple  point  C  we  have  the  three  phases  in  equi- 
librium. If  the  system,  solid-liquid-vapor,  be  heated,  the 
solid  phase  will  disappear  first  and  the  equilibrium  between 
liquid- vapor  will  be  produced ;  and  if  heat  be  continually 
added,  the  system  will  take  the  direction  represented  by  the 
curve  CB.  If  the  system  be  cooled,  the  liquid  water  will 
disappear  and  the  equilibrium  will  be  described  by  the 
curve  CD,  which  represents  the  equilibrium  between  ice 
and  vapor. 

The  triple  point  C  for  water  is  not  exactly  o°  C.,  as  the 
melting  point  is  defined  as  o°  under  a  pressure  of  760  mm. 
This  ice  is  under  its  own  vapor  pressure,  which  is  nearly  4.6 
mm.,  or  practically  one  atmosphere  less.  From  Table 
XXXIV,  which  gives  the  fusion  pressure  of  ice  for  pressure 
as  high  as  about  2000  atmospheres,  it  is  found  that  an  in- 
crease of  one  atmosphere  lowers  the  melting  point  of  ice 
0.0075°,  *"•£•  it  would  require  134  atmospheres  to  change  the 
melting  point  i°  C. 


PHASE  RULE  189 

TABLE  XXXIV  —  FUSION  PRESSURE  OF  ICE 


TEMP. 

PRESSURE  IN  KILOGRAMS 
PER  SQ.  CM. 

CHANGE  OF  MELTING  PT. 
PER  INCREASE  OF 
i  KILOGRAM  PER  SQ.  CM. 

o°C. 

-  5 

o  (4.6  mm.) 
610 

0.0072 
0.0087 

—   IO 

-  15 

1130 
1590 

O.OIO2 
O.OIlS 

—  20 

1970 

0.0135 

Polymorphism.  —  We  have  been  considering  the  physical 
forms  of  matter,  i.e.  the  different  phases  due  to  the  change 
in  pressure  and  temperature.  Whether  water  exists  in  the 
solid,  liquid,  or  vapor  phase  depends  upon  the  pressure  and 
temperature  to  which  it  is  subjected.  It  is  known  that 
certain  substances  exist  in  only  one  vapor,  one  liquid,  and 
one  solid  phase ;  but  many  other  substances  exist  in  four  or 
more  different  phases.  For  example,  sulphur  exists  in  at 
least  four  phases :  two  solid,  one  liquid,  and  one  vapor. 
The  same  is  true  of  a  large  number  of  other  substances. 
The  solid  phases  are  always  different  in  crystalline  form,  the 
melting  points  are  different,  as  well  as  the  specific  gravity 
and  a  number  of  other  physical  properties.  This  phenom- 
enon is  known  as  polymorphism  and  was  recognized  by 
Mitscherlich  as  early  as  1820  in  the  cases  of  disodium 
hydrogen  phosphate  and  of  sulphur.  Formerly  polymor- 
phism was  considered  a  very  rare  thing,  but  so  many  cases 
have  now  been  observed  that  it  is  considered  the  rule  rather 
than  the  exception.  When  an  element  exists  in  more  than 
one  form  or  modification  it  is  said  to  exhibit  allotropy,  and 
the  forms  or  modifications  are  termed  allotropes  or  allotropic 
modifications.  When  compounds  exhibit  this  phenomenon 
it  is  termed  polymorphism,  and  depending  on  the  number  of 
crystalline  forms,  the  compound  is  said  to  be,  for  two  forms, 


190  PHYSICAL   CHEMISTRY 

dimorphous ;  for  three,  trimorphous ;  for  four,  tetrarhor- 
phous.  The  term  polymorphism  is  frequently  applied  to 
both  compounds  and  elements,  but  does  not  include  the 
allotropy  of  amorphous  substances,  such  as  ozone,  or  of 
liquid  sulphur. 

Types  of  Polymorphism  or  Allotropy.  —  The  different 
allotropic  modifications  of  substances  have  different  and 
distinct  physical  properties :  crystalline  form,  melting 
point,  rate  of  expansion,  conductivity  of  both  heat  and 
electricity,  color,  etc. 

The  transformation  of  a  substance  from  one  phase  into 
another  takes  place  at  constant  temperature  for  a  given 
pressure.  This  is  illustrated  by  the  change  of  liquid  water 
into  ice,  where  we  have  the  appearance  of  a  new  phase  and 
the  two  phases  coexisting  in  equilibrium ;  or  at  very  high 
pressures  the  reverse  change  may  occur.  The  conditions 
of  temperature  and  pressure  under  which  the  change  of 
one  phase  into  another  occurs  or  where  a  new  phase  appears 
and  coexists  in  equilibrium  with  the  others  is  termed  the 
transition  point.  The  temperature  at  which  this  occurs  is 
the  transition  temperature,  and  the  pressure,  the  transition 
pressure,  which,  however,  may  vary  over  wide  ranges 
without  appreciably  affecting  the  temperature  of  equilib- 
rium, and  as  a  result  is  many  times  neglected,  particu- 
larly in  the  case  of  such  transitions  as  that  of  a  iron  into 
/3  iron.  The  transition  point  is  also  called  the  inversion 
point. 

The  three  following  types  of  polymorphic  or  allotropic 
substances  exist : 

I.  Enantiotropic  substances  are  those  whose  polymorphic 
forms  may  be  directly  transformed  one  into  the  other,  and 
the  transition  point  lies  below  the  melting  point  of  each  of 
the  forms. 

In  Table  XXXV  are  listed  a  few  well-marked  examples  of 
enantiotropic  polymerization  among  inorganic  substances. 


PHASE   RULE 
TABLE  XXXV 


191 


SUBSTANCES 

FORMS 

TRANSITION 
TEMPERATURE 

Fe 

/                             a^P 

\                              ^^±T 

780° 
920 

S 

Rhombic  ^f.  Monoclinic 

95-5 

Sn 

J                 Gray  ^  Tetragonal 
I       Tetragonal  ^  Rhombic 

18 
'161 

Zn 

f                         «^t/3 
I                           /3^±T 

170 
340 

Agl 

Hexagonal  ^fH  Regular 

H7 

AgN03 

Rhombic  ^  Rhombohedral 

159-5 

As2S2 

Red  ^±  Black 

267 

Ca2SiO4 

7^/3 

675 

/^« 

1420 

HgI2 

Tetragonal  ^  Rhombic 

126 

KNO3 

Rhombic  !^  Rhombohedral 

129.5 

K2SO4 

Rhombic  ^  Hexagonal 

599 

Tetragonal  ^  a  rhombic 

-16 

a  rhombic  ^  0  rhombic 

35 

NH4N03 

/3  rhombic  ^  Hexagonal 
rhombohedral 
Hexagonal 
.  rhombohedral  Ze^  Regular 

85-4 
125 

SiO2 

Quartz  <*  Tridymite 

800 

T1NO3 

[           Rhombic  <*  Rhombohedral 
1  Rhombohedral  <*  Regular 

728 
142-5 

II.  Monotropic  Substances,  Iodine  monochloride  is  known 
in  two  forms  :  a-ICl  which  melts  at  27.2°,  and  /3-IC1  which 
melts  at  13.9°,  the  a  form  being  the  stable  form  at  ordi- 
nary temperature.  These  do  not  exhibit  a  transition  period 
nor  are  they  directly  transformable  one  into  the  other. 
A  number  of  substances  manifest  this  phenomenon  of  not 


I Q2  PHYSICAL   CHEMISTRY 

being  reversibly  transformable  and  polymorphism  of  this 
irreversible  kind  is  termed  monotropy. 

III.  Dynamic  Allotropy.  It  is  known  that  two  of  the 
liquid  forms  of  sulphur,  S\  and  SM,  can  exist  together  in 
definite  proportions,  which  depend  on  the  temperature. 
This  phenomenon  is  termed  dynamic  allotropy.  The  various 
solid  polymorphic  forms  cannot  exist  together  except  at  the 
transition  point,  but  those  manifesting  dynamic  allotropy 
can  do  so,  and  this  is  explained  on  the  basis  of  the  existence 
of  molecules  of  different  complexity. 

Smith  and  his  colaborers  have  shown  that  the  two  liquid 
phases  of  sulphur,  SA  and  SM,  have  different  solubilities 
in  a  number  of  different  solvents :  diphenylmethane,  di- 
phenyl,  /?-naphthol  and  triphenylmethane ;  SA  dissolves 
in  these  solvents  with  an  absorption  of  heat  as  shown  by  the 
ascending  curve  of  solubility,  while  S^  dissolves  with  evolu- 
tion of  heat  as  shown  by  the  descending  curve  of  solubility. 

Many  substances  that  manifest  polymorphism  have  labile 
modifications  that  exist  at  temperatures  far  below  the  transi- 
tion point  or  inversion  temperature  as  in  the  case  of  calcite 
and  aragonite,  the  two  solid  modifications  of  calcium  car- 
bonate. On  heating,  aragonite  changes  to  calcite,  but  at 
ordinary  temperatures  the  two  forms  exist  in  apparent 
stable  equilibrium.  In  the  case  of  carbon  the  three  modifi- 
cations exist  together  under  ordinary  conditions  of  tem- 
perature and  pressure,  which  is  possibly  due  to  the  high 
inversion  temperature.  The  same  is  probably  true  in  the 
case  of  titanic  acid  and  many  others. 

ONE  COMPONENT  SYSTEM  —  SULPHUR 

The  p-t  diagram  for  sulphur  is  represented  in  Fig.  36. 
Sulphur  exists  in  two  solid  crystalline  forms,  the  rhombic, 
stable  below  95.5°,  and  the  monoclinic,  the  stable  form, 
between  95.5°  and  120°. 


PHASE   RULE 


193 


Vapor 


IlA      120*151* 

Sulphur 

FIG.  36. 


This  figure  will  probably  be  more  readily  understood  if  it 
is  redrawn,  first  drawing  the  p-t  diagram  for  rhombic  sulphur 
and  then  drawing  the  p-t  diagram  for  monoclinic  sulphur 
superposed  upon  this  with  the 
melting  point  of  monoclinic  sulphur 
(120°)  located  upon  the  vapor  pres- 
sure curve  for  rhombic  sulphur. 

Applying  the  phase  rule  to  the 
various  systems  represented  by  the 
areas,  lines,  and  points  as  we  did 
in  the  case  of  the  p-t  diagram  for 
water  we  would  have : 

I.  Fields    or    areas.      Here    we 
have   one  phase.     Then  from  the 

Phase  Rule,  N  —  P  +  2  =  F,  substituting,  we  have  i  —  i 
+  2  =  2.  Therefore  the  areas  represent  divariant  systems. 
There  are  four  of  these : 

1.  Area  under  line  EFCB  —  sulphur  vapor 

2.  Area  to  the  right  of  BCGH  —  liquid  sulphur 

3.  Area  to  left  of  EFGH  —  rhombic  sulphur 

4.  Area  of  the  triangle  GFC  —  monoclinic  sulphur 

II.  Curves.     According    to    the    Phase    Rule   we    have, 
1  —  2  +  2  =  1,  therefore  monovariant  systems: 

1 .  Curve  EF  —  rhombic-vapor 

2 .  Curve  FC  —  monoclinic -vapor 

3.  Curve  CB  —  liquid-vapor 

4.  Curve  CG  —  monoclinic-liquid 

5.  Curve  GH  —  rhombic-liquid 

6.  Curve  FG  —  rhombic-monoclinic 

III.  At  the  intersection  of  some  of  these  curves  we  have 
three  phases  in  equilibrium,  and  according  to  the  Phase 
Rule  we  have  1—3  +  2=0;  therefore  nonvariant  systems. 
These  are  called  triple  points. 

1 .  Point  F  —  rhombic-monoclinic-vapor 

2 .  Point  C  —  monoclinic-liquid-vapor 


IQ4  PHYSICAL  CHEMISTRY 

3 .  Point  G  —  rhombic-liquid-monoclinic 

4.  Point  A  —  rhombic-monoclinic-vapor  is  a  condition  of 
labile  equilibrium  and  is  not  readily  realized. 

The  intersection  of  the  two  sublimation  curves  at  F 
represents  the  transition  point  95.5°  at  which  rhombic  and 
monoclinic  sulphur  are  in  equilibrium.  Below  this  tempera- 
ture rhombic  sulphur  has  the  lower  vapor  pressure  and  is  the 
stable  form,  while  above  this  temperature  monoclinic  sul- 
phur is  the  stable  form. 


CHAPTER  XVIII 


SOLUTION   OF   SOLIDS  IN   LIQUIDS— I 

THE  solubility  of  a  solid  in  a  liquid  depends  upon  the 
nature  of  the  solvent  as  well  as  upon  the  solute.  The  solu- 
bility is  also  usually  greatly  affected  by  the  temperature, 
but  the  pressure  does  not  have  such  a  marked  effect. 

In  Figs.  37  and  38  we  have  represented  the  change  in  the 
solubility  of  solids  in  water  with  changes  in  temperature. 
These  are  termed  temperature-concentration  diagrams. 

Generally  speaking,  the  analogous  compounds  of  the  ele- 
ments of  the  same  family,  if  arranged  in  the  order  of  their 


FIG.  37- 


FIG.  38. 


solubility,  will  be  found  to  be  in  the  increasing  or  the  de- 
creasing order  of  their  atomic  weights. 

Cs,  Rb,  K,  Na,  Li,  with  decreasing  order  of  atomic  weights, 
have  increasing  solubility  of  their  chlorides  and  nitrates. 
This  does  not  hold  absolutely. 

These  solubility  curves  are  equilibrium  curves  and  rep- 
resent the  equilibrium  between  the  solid  salt  and  the  solu- 
tion, which  is  saturated  with  respect  to  the  solid  phase 
separating.  A  saturated  solution  is  then  a  solution,  at  a 
specified  temperature,  in  equilibrium  with  the  solid  phase. 


196  PHYSICAL   CHEMISTRY 

If  we  have  two  curves,  as  in  Fig.  37,  A B  must  represent  the 
solubility  of  one  chemical  individual  and  BC  that  of  another. 
That  is,  along  the  line  A  B  a  different  solid  phase  separates 
than  along  the  line  BC.  Below  the  curve  A  B  we  have  un- 
saturated  solutions,  and  on  the  curve,  saturated,  and  above, 
supersaturated  solutions.  In  all  solubility  work  we  must 
consider  what  solid  is  in  equilibrium  with  the  solution,  and 
since  many  salts  separate  with  water  of  crystallization,  we 
may  have  the  same  solubility  at  different  temperatures. 
It  must  be  remembered  that  a  solution  is  saturated  with 
respect  to  a  particular  substance  only  when  it  is  in  equilib- 
rium with  that  particular  substance  at  the  specified  tem- 
perature. 

The  solubility  of  organic  substances,  likewise,  depends 
upon  the  solvent  and  the  solute,  that  is,  upon  the  chemical 
character  of  both.  In  water,  almost  all  substances  con- 
taining the  hydroxyl  group  (OH)  dissolve  more  or  less 
readily,  e.g.  the  alcohols.  In  the  case  of  organic  acids,  the 
solubility  of  the  members  of  a  homologous  series  decreases 
as  the  carbon  content  increases  (e.g.  formic,  acetic,  propionic, 
butyric).  The  solubility  of  the  higher  members  of  the 
series  is  small.  Benzene,  C6H6,  is  insoluble  in  water  ;  phenol, 
C6H6OH,  is  soluble  to  the  extent  of  about  two  per  cent  in 
water ;  while  dihydric  phenols,  C6H4(OH)2,  are  very  soluble, 
and  trihydric  phenols,  C6H3(OH)3,  are  miscible  in  all  propor- 
tions with  water.  Following  the  analogy,  practically  all 
alcohols  are  soluble  in  alcohol  and  all  acids  in  acetic  acid, 
all  hydrocarbons  in  benzene,  etc.  An  effort  has  been  made 
by  Carnelly  and  Thomson  (Jour.  Chem.  Soc.  53,  782  (1888)) 
to  formulate  some  rules  for  the  solubility  of  substances,  and 
they  make  the  following  general  statements : 

i.  That  for  any  series  of  isomeric  organic  compounds 
the  order  of  solubility  is  the  same  as  the  order  of  fusibility : 
the  most  fusible  is  the  most  soluble.  Taking  all  solvents 
into  account,  1755  out  of  1778  cases  hold. 


SOLUTION  OF  SOLIDS   IN  LIQUIDS  197 

2.  In  any  series  of  isomeric  acids  not  only  is  the  order 
of  solubility  of  the  acids  themselves  the  same  as  the  order 
of  fusibility,  but  the  same  order  of  solubility  extends  to  all 
the  salts  of  the  second  acids,  so  that  the  salts  of  the  more 
soluble  and  more  fusible  acids  are  also  more  easily  soluble 
than  the  corresponding  salts  of  the  less  fusible  and  less 
soluble  acids.     Five  exceptions  out  of  143  cases  were  found. 

3.  For  any  series  of  isomeric  compounds  the  order  of 
solubility  is  the  same  no  matter  what  may  be  the  nature 
of  the  solvent.     No  exception  to  this  was  found  out  of  666 
cases. 

4.  The  ratio  of  the  solubilities  of  the  two  isomerides  in 
any  given  solvent  is  very  nearly  constant,  and  is  therefore 
independent  of  the  nature  of  the  solvent. 

Pitch  of  Solubility  Curve.  —  In  the  pitch  of  the  solubility 
curve  one  has  some  criterion  as  to  the  true  heat  of  solution 
of  the  particular  substance.  By  inspecting  a  solubility  curve 
the  sign  of  the  heat  effect  involved  in  the  solution  of  the 
substance  can  be  ascertained.  If  the  substance  dissolves 
with  an  absorption  of  heat,  it  will  dissolve  in  greater  quan- 
tity as  the  temperature  is  increased.  Most  inorganic  salts 
dissolve  in  water  with  absorption  of  heat,  and  their  solu- 
bility increases  with  an  increase  in  the  temperature.  Ex- 
amples are  NH4NO3  and  NH4CNS.  A  number  of  salts 
dissolve  with  the  evolution  of  heat,  and  their  solubility  de- 
creases with  increase  in  temperature;  examples  are  most 
anhydrous  sulphates,  calcium  isobutyrate,  etc.  We  have 
a  large  number  of  salts,  intermediate  between  these  two 
classes,  which  dissolve  with  practically  no  heat  effect,  and 
the  solubility  of  which  is  nearly  constant  for  wide  ranges  of 
temperature.  Common  salt,  NaCl,  is  an  example  of  this 
class. 

We  must  not  fail  to  distinguish  between  the  heat  of  solu- 
tion usually  determined  in  thermo-chemistry  and  the  true 
heat  of  solution,  or  perhaps  it  had  better  be  called  the 


198  PHYSICAL   CHEMISTRY 

heat  of  precipitation,  which  has  the  opposite  sign.  By 
heat  of  solution  or  heat  of  precipitation  we  mean  the  heat 
effect  when  the  solute  is  added  to  an  almost  saturated  solu- 
tion. The  heat  of  solution  in  the  thermo-chemical  sense  is 
the  heat  effect  when  the  solute  is  dissolved  in  a  large  amount 
of  water  and  is  very  much  more  easily  measured  than  the 
heat  of  precipitation.  Calcium  isobutyrate  below  80° 
dissolves  in  a  large  quantity  of  water  with  evolution  of 
heat,  in  a  little  water  with  absorption  of  heat.  Cupric 
chloride  dissolves  in  a  large  amount  of  water  with  evolu- 
tion of  heat,  and  this  heat  effect  decreases  as  the  quantity 
of  water  used  is  decreased.  In  nearly  saturated  solutions 
the  heat  of  solution  changes  sign  and  we  have  an  absorption 
of  heat. 

It  follows  then  that  there  must  be  some  quantity  of  water 
in  which  a  definite  quantity  of  the  salt  will  dissolve  without 
either  evolution  or  absorption  of  heat.  This  has  been  veri- 
fied experimentally  in  the  case  of  the  hydrates  of  FeCla. 
The  heat  of  precipitation  of  NaCl  is  very  nearly  zero,  and 
consequently  the  change  in  the  solubility  of  this  salt  with 
the  increase  in  temperature  is  very  slight.  So  one  can 
tell  very  readily  the  sign  of  the  heat  effect  from  the  solu- 
bility curves,  providing  they  are  continuous  curves.  But 
if  a  curve  has  a  break  in  it  at  some  point,  a  discontinuity, 
we  know  that  some  change  has  taken  place,  —  probably  in 
the  phases  in  contact  with  the  solution.  Hence  any  such 
sharp  discontinuity  will  lead  us  to  suspect  that  there  is  a 
change  in  the  phase  relations.  As  we  have  a  number  of  such 
cases  coming  under  the  head  of  hydrates  we  shall  defer  their 
treatment. 

THEOREM  OF  LE  CHATELIER 

We  have  seen  that  the  results  of  the  determinations  of 
the  effect  of  pressure  on  the  fusion  point  of  ice  show  that 
the  temperatures  at  which  the  solid  and  liquid  are  in  equilib- 


SOLUTION  OF  SOLIDS  IN  LIQUIDS  199 

rium  are  below  the  triple  point.  Ice  has  a  lower  density 
than  liquid  water,  showing  that  the  most  dense  phase  of 
water  is  liquid  water,  hence  when  the  system  is  subjected 
to  pressure  it  will  tend  to  compensate  for  this  external  pres- 
sure by  readjusting  itself  so  as  to  occupy  a  smaller  volume, 
and  if  we  have  ice  present  this  increased  pressure  will  result 
in  liquefying  the  ice,  and  the  system  will  occupy  a  smaller 
volume.  If,  however,  the  temperature  at  which  the  solid 
and  liquid  are  in  equilibrium  is  above  the  temperature  of 
the  triple  point,  the  substance  has  a  greater  density  in  the 
solid  than  in  the  liquid  state,  and  increased  pressure  will 
tend  to  cause  the  system  to  pass  into  the  solid  state  which 
is  the  most  dense.  For  substances  in  general,  the  solid  is 
the  most  dense  phase.  Water  is  one  of  the  few  exceptions 
to  this  general  rule. 

In  the  case  of  benzene  the  most  dense  phase  is  the  solid. 
Hence  an  increase  in  the  pressure  will  cause  the  freezing 
point  to  rise,  and  the  fusion  curve  will  slant  away  from  the 
pressure  axis  toward  the  right.  If  benzene  is  subjected  to 
3742.7  mm.  pressure,  the  melting  point  will  be  raised  0.143°. 

This  fact,  that  by  means  of  an  increase  in  pressure  the 
most  dense  phase  of  the  substance  tends  to  form,  represents 
one  of  the  most  fundamental  laws.  This  law  has  its  coun- 
terpart in  the  Law  of  Motion,  that  action  and  reaction  are 
equal  and  in  the  opposite  direction.  This  is  known  in 
chemistry  as  the  Theorem  of  Le  Chatelier  and  may  be  ex- 
pressed as  follows :  "  Any  change  in  the  factors  of  equi- 
librium from  outside  is  followed  by  an  inverse  change  inside 
the  system  ; "  i.e.  there  is  a  change  in  the  factors  of  equilib- 
rium tending  to  restore  equilibrium. 

Hence  by  increasing  the  external  pressure  on  a  system  there 
would  be  an  increase  of  that  component  or  phase  occupy- 
ing the  least  volume ;  or  if  heat  is  added,  we  have  an  increase 
of  that  component  or  phase  which  involves  an  absorption 
of  heat.  Hence  a  system  in  equilibrium  tends  to  return 


200  PHYSICAL   CHEMISTRY 

to  equilibrium  by  eliminating  the  disturbing  element. 
Ammonium  chloride  dissolves  with  expansion,  and  the 
solubility  is  diminished  about  one  per  cent  by  increasing 
the  pressure  to  160  atmospheres.  Copper  sulphate  dis- 
solves with  contraction,  and  the  solubility  increases  3.2  per 
cent  on  increasing  the  pressure  to  60  atmospheres.  Sodium 
sulphate  with  10  molecules  of  water  of  crystallization  dis- 
solves with  absorption  of  heat,  hence  the  solubility  increases 
with  an  increase  in  temperature.  All  of  these  facts  are  in 
accord  with  the  Theorem  of  Le  Chatelier. 

If  a  system  is  in  equilibrium  at  a  specified  temperature 
and  heat  be  applied,  there  will  be  a  tendency  to  compensate 
for  this  heat  added  to  the  system  by  a  readjustment  within 
the  system  either  through  a  physical  adjustment,  such  as 
increase  of  the  volume  if  the  pressure  remains  constant,  or 
by  an  increase  of  pressure  in  order  to  maintain  the  volume 
constant.  Or  if  this  addition  of  heat  results  in  the  com- 
pensating change  through  a  chemical  reaction,  such  as  the 
formation  of  ozone  from  oxygen,  or  in  the  preparation  of 
nitric  oxide,  carbon  bisulphide,  acetylene,  etc.,  or  the  dis- 
sociation of  calcium  carbonate,  we  shall  have  either  an  ab- 
sorption of  heat  or  an  evolution  of  heat,  depending  upon 
the  particular  type  of  reaction  that  is  taking  place  under  our 
specified  conditions.  In  most  cases  of  dissociation  the  in- 
crease in  dissociation  is  associated  with  an  absorption  of 
heat,  that  is,  it  is  an  endothermic  reaction.  For  as  heat  is 
applied  the  reaction  proceeds,  and  being  accompanied  by 
an  absorption  of  heat,  the  heat  from  the  outside  of  the 
system  has  to  be  applied  to  maintain  the  system  at  a  con- 
stant temperature,  so  that  a  rise  in  temperature  favors  the 
formation  of  the  products  of  the  reaction.  Ozone  is  pre- 
pared according  to  the  equation  3  O2  =  2  O3,  and  the  re- 
action is  accompanied  by  an  absorption  of  heat.  It  is  an 
endothermic  reaction,  and  therefore  the  percentage  of 
ozone  formed  increases  with  the  rise  in  temperature.  If 


SOLUTION   OF  SOLIDS   IN  LIQUIDS  2OI 

the  reaction  evolves  heat  it  is  said  to  be  exothermic  and 
takes  place  best  with  a  decrease  in  temperature. 

The  inversion  temperature  at  which  the  rhombohedral 
form  of  NH4NO3  can  be  transformed  into  the  /?-rhombic 
form  can  be  changed  from  85.45°  under  a  pressure  of  one 
atmosphere  to  82.29°  by  increasing  the  pressure  to  250  at- 
mospheres. 

The  following  geological  application  of  the  Theorem  of 
Le  Chatelier  worked  out  by  Van  Hise  is  a  marked  confirma- 
tion of  this  principle.  In  the  outer  zone  of  the  earth's  crust 
there  takes  place  the  metamorphic  changes  of  the  minerals, 
such  as  the  alteration  of  the  silicates  by  means  of  hydration, 
carbonation,  and  desilicification,  which  are  accompanied 
by  a  liberation  of  heat,  decrease  in  the  density,  and  an  in- 
crease in  the  volume.  This  region  is  known  as  the  Zone 
of  Katamorphism,  and  in  it  the  average  specific  gravity  of 
the  minerals  is  2.948.  In  the  inner  zone  of  metamorphism, 
a  few  thousand  feet  from  the  surface  of  the  earth,  where 
there  is  an  increased  pressure  due  to  the  overlying  rocks, 
there  is  also  a  much  higher  temperature  than  in  the  outer 
zone  of  metamorphism.  This  inner  region  is  known  as  the 
Zone  of  Anamorphism,  and  we  have  the  alteration  of  the 
minerals  due  to  dehydration,  decarbonation,  and  silicifica- 
tion,  which  are  accompanied  by  an  absorption  of  heat  and 
condensation  of  volume,  which  are  the  typical  changes. 
The  average  specific  gravity  of  the  minerals  in  the  Zone  of 
Anamorphism  is  3.488,  which  is  about  18  per  cent  higher 
than  that  of  the  minerals  in  the  Zone  of  Katamorphism. 
This  is  a  fair  approximation  and  shows  that  a  given  mass 
of  material  occupies  a  much  larger  volume  in  the  Zone  of 
Katamorphism  than  in  the  Zone  of  Anamorphism. 

A  few  special  examples  will  serve  to  illustrate  this.  The 
change  of  hematite  into  limonite  may  be  represented  by  the 
equation  2  Fe20s  +  3  H2O  =  2  Fe2O3  •  3  H2O.  This  reaction 
takes  place  in  the  Zone  of  Katamorphism  and  is  one  of 


202  PHYSICAL   CHEMISTRY 

hydration.  The  specific  gravity  of  hematite  is  5.225  and 
of  limonite  3.80,  which  change  represents  an  increase  in 
volume  of  60.7  per  cent.  One  of  the  most  common  and  best 
known  alterations  is  hematite  into  siderite.  This  may  be 
represented  as  follows : 

Fe2O3  +  2H2S  +  CO2  =  FeSa  +  FeCO3  +  2  H2O  +  k  cal. 
If  the  products  of  alteration  are  pyrite  (isometric,  sp.gr. 
5.025)  and  siderite  (sp.gr.  3.855),  the  increase  in  volume  is 
76  per  cent ;  but  if  marcasite  (orthorhombic,  sp.gr.  4.875)  is 
formed  instead  of  pyrite,  the  increase  in  volume  of  mar- 
casite and  siderite  over  the -hematite  is  78.7  per  cent.  The 
most  marked  case  known  in  which  minerals  are  concerned 
is  the  alteration  of  magnetite  into  siderite.  The  equation 
Fe304  +  CO  +  2  CO2  =  3  FeCO3  represents  the  alteration 
which  gives  a  change  of  specific  gravity  from  5.74  for  mag- 
netite to  2.83  for  siderite,  which  represents  the  enormous 
increase  in  volume  of  101  per  cent.  These  changes  all  take 
place  with  the  liberation  of  heat,  expansion  of  volume,  and 
decrease  in  symmetry. 

As  a  typical  example  of  deep-seated  reactions  under  great 
pressure  and  high  temperature,  the  change  of  calcite  into 
wollastonite  is  one  that  is  well  known,  CaCO3  +  SiO2  = 
CaSiO3  +  CO2  —  k  cal.  Here  we  have  a  change  in  specific 
gravity  from  2.713  for  calcite  and  2.655  f°r  SiO2  to  2-&5  for 
wollastonite,  which  represents  a  decrease  in  volume  of  31.5 
per  cent  provided  the  silica  is  solid  and  the  carbon  dioxide 
escapes.  We  have,  as  in  all  other  deep-seated  reactions,  an 
absorption  of  heat  and  condensation  of  volume  as  the  typical 
changes  in  the  Zone  of  Anamorphism. 

The  same  principles  are  clearly  illustrated  in  the  case  of 
the  alteration  of  silicates,  which  are  brought  up  by  means 
of  some  erogenic  movement  to  the  surface  of  the  earth  or 
near  to  it.  This  alteration  of  the  silicates  by  hydration, 
carbonation,  and  desilicification  is  attended  with  the  con- 
comitant liberation  of  heat,  a  decrease  in  the  specific  grav- 


SOLUTION  OF  SOLIDS  IN  LIQUIDS  203 

ity,  and  a  marked  increase  in  the  volume.  The  alteration  of 
garnets  into  different  combinations  of  the  following  minerals 
is  well  known:  serpentine,  talc,  chlorite,  epidote,  zoisite, 
magnesite,  and  gibbsite. 

The  following  equation,  which  is  typical  of  these  trans- 
formations, will  suffice  to  illustrate  the  marked  change 
which  amounts  in  this  case  to  an  increase  in  volume  of  76 
per  cent : 

+  15  H2O  +  3  C02 


pyrope 
sp.gr.  3.725 


3  H2Mg3Si4012  +  3  MgC03  +  8  A1(OH)3  +  k  cal. 

talc  magnesite  gibbsite 

sp.gr.  2.75  sp.gr.  3.06          sp.gr.  2.35 


CHAPTER  XIX 
SOLUTION  OF   SOLIDS  IN   LIQUIDS  — II 

THE  SOLVENT  AND  SOLUTE  CRYSTALLIZE  TOGETHER  AS  A 
MIXTURE  OF  THE  PURE  COMPONENTS 

IN  the  two  component  systems  in  which  we  have  a  liquid 
solvent,  and  a  solid  solute,  we  assume  that  the  vapor  pressure 
of  the  solid  is  so  small  that  it  is  negligible,  so  that  in  the 
systems  we  are  to  consider  one  of  the  components  is  non- 
volatile and  one  volatile.  There  are  three  general  types  of 
such  systems : 

Type  I.  The  solvent  and  solute  may  crystallize  together 
as  a  mixture  of  the  pure  components. 

Type  II.  The  solvent  and  solute  crystallize  in  accordance 
with  the  Laws  of  Definite  and  Multiple  Proportions. 

Type  III.  The  solvent  and  solute  crystallize  together  not 
in  accordance  with  the  Laws  of  Definite  and  Multiple  Pro- 
portions, but  as  solid  solute  dissolved  in  a  solid  solvent  in 
varying  proportions,  within  certain  limits. 

TYPE  I  —  SYSTEM  WATER  AND  SODIUM  CHLORIDE 

At  the  intersection  of  the  vapor  pressure  and  sublimation 
curves  for  pure  water,  the  solid,  liquid,  and  vapor  phases  are 
in  equilibrium,  and  we  designate  this  the  fusion  point  of 
ice,  or  the  transition  point.  As  these  phases  are  in  equilib- 
rium under  the  pressure  of  the  vapor  of  the  system,  it  is  a 
pressure  of  4.6  mm.  and  at  the  temperature  +  0.0075°  C. 
The  freezing  point  of  liquids  is  the  temperature  at  which  the 

204 


SOLUTION   OF  SOLIDS   IN   LIQUIDS  205 

solid  and  liquid  phases  are  in  equilibrium  under  atmospheric 
pressure,  which  in  the  case  of  water  would  be  under  nearly 
one  atmosphere  pressure  more  than  at  the  transition  temper- 
ature. As  an  increase  in  pressure  of  one  atmosphere  lowers 
the  melting  point  of  ice  0.0076°,  it  is  apparent  that  the  fusion 
point,  freezing  point,  and  transition  point  may  be  considered 
the  same.  On  thep-t  diagram,  Fig.  39, 
let  us  represent  the  one-component 
systems  by  the  following  dotted  lines. 

A  B  is  the  vapor  pressure  curve 

AC  is  the  sublimation  curve 

AD  is  the  fusion  curve 

A  is  the  triple  point  and  represents 


the  melting  point  of  ice  and  the  freezing  pIG  39< 

point  of  water. 

If  a  second  component,  solid  salt,  NaCl,  be  added  to 
water,  the  vapor  pressure  of  the  solution  produced  is  lower 
than  the  vapor  pressure  of  the  pure  solvent  water,  and  the 
amount  of  the  lowering  of  the  vapor  pressure  is  proportional 
to  the  concentration.  By  adding  successive  amounts  of 
NaCl  the  vapor  pressures  of  the  solutions  would  be  rep- 
resented by  vapor  pressure  curves  parallel  to  AB,  but 
successively  lower  until  we  would  reach  a  concentration 
representing  the  maximum  amounts  of  salt  that  are  soluble 
at  the  different  temperatures,  when  we  would  have  saturated 
solutions,  the  vapor  pressures  of  which  we  represent  by  CF. 
This  represents  the  maximum  lowering  of  the  vapor  pressure 
of  the  pure  water.  If  these  vapor  pressure  curves  are  pro- 
jected until  they  intersect  the  freezing  point  curve,  we  have 
the  point  A,  the  intersection  of  the  vapor  pressure  curve 
and  the  sublimation  curve,  passing  down  successively  to  the 
point  C,  its  lowest  limit.  Similarly,  the  curve  AD,  the 
fusion  curve,  would  pass  over  the  space  to  the  left  of  its 
original  position  and  take  up  as  its  final  position,  CE.  A, 
the  freezing  point  of  pure  water,  has  been  lowered  from  the 


206  PHYSICAL   CHEMISTRY 

temperature  o°  to  the  temperature  tc,  and  the  distance  along 
the  temperature  axis  represents  the  maximum  lowering  of 
the  freezing  point. 

The  degree  of  variance  of  this  two-component  system  may 
be  obtained  by  applying  the  Phase  Rule  as  follows : 

I.  Areas.    (N  —  P  +  2  =  F),  2  —  2  +  2  =  2.'.  Divariant 
systems : 

1 .  Salt-vapor  below  GCF  and  above  /-axis. 

2.  Solution- vapor  between  BACF. 

3.  Solution-ice  between  DACE. 

4.  Ice-salt  between  ECG  and  £-axis. 

II.  Curves.     (N  -  P  +  2  =  F),  2  -  3  +  2  =  i  .'.  Mono- 
variant  systems : 

1.  CF  Solution-vapor-salt. 

2.  CE  Solution-ice-salt. 

3.  CG   Ice-salt-vapor. 

-4.   CA  Solution-ice-vapor. 

III.  Point  C.    (N  -  P  +  2  =  F),  2  -  4  +  2  =  o  /.  Non- 
variant  system. 

At  point  C  the  four  phases,  solution-salt  ice-vapor,  are  in 
equilibrium.  This  is  known  as  a  Quadruple  Point. 

If  a  body  in  the  liquid  state  be  allowed  to  cool  without 
change  of  state,  and  measurement  of  the  temperature  be 
made  at  different  times,  and  these  results  plotted  on  a 
temperature-time  axis,  the  curve  has  a  regular  form  —  a 
logarithmic  curve  when  the  cooling  takes  place  for  constant 
temperature  surroundings.  But  if  a  change  of  state  occurs, 
there  is  a  decided  change  in  the  shape  of  the  curve.  In  all 
cases  observed  the  passage  of  a  liquid  to  a  solid  is  accom- 
panied by  the  evolution  of  heat.  This  heat  liberated  com- 
pensates for  loss  of  heat  by  radiation  and  maintains  the 
temperature  constant,  the  solid  separating  and  the  process 
continuing  until  the  whole  of  the  liquid  has  changed  to  the 
solid  state,  when  the  temperature  changes  become  regular 
again. 


SOLUTION  OF  SOLIDS   IN  LIQUIDS 


207 


In  Fig.  40  we  have  an  illustration  of  the  continuous  cooling 
curve  without  change  of  state,  while  Fig.  41  illustrates  the 
cooling  curves  of  a  number  of  pure  substances.  These  show 
a  marked  break  at  the  temperature  of  the  melting  point  of 


Time 

FIG.  40. 


Time 

FIG.  41. 


the  substance ;  above  and  below  this  the  temperature  falls 
regularly,  but  at  this  point  the  temperature  remains  con- 
stant until  all  of  the  substance  has  solidified. 

The  cooling  curves  for  two  component  systems,  such  as 
solutions  of  sodium  chloride  in  water,  differ  from  that  of  a 
pure  substance.  For  when  solidification  begins,  either  of 
the  two  components  may  separate,  depending  upon  the 
concentration  of  the  solution.  At  the  point  of  solidification 
we  have  a  marked  break  in  the  cool- 
ing curve,  the  separation  of  the  pure 
component,  which  results  in  a  change 
in  the  concentration  of  the  solution 
with  a  lowering  of  the  freezing  point. 
Hence,  on  a  t-time  diagram  for  a 
solution  of  the  concentration  of  ten 
per  cent  of  sodium  chloride,  we  should 
have  the  regular  cooling  of  the  solution, 
as  represented  by  ab  in  Fig.  42,  until 
at  the  point  6,  the  solid  water  (ice)  begins  to  separate,  and 
we  have  a  change  in  the  slope  of  the  cooling  curve.  This 
separation  of  the  ice  continues  until  the  point  c  is  reached, 
when  the  remainder  of  the  solution  solidifies  completely. 


Time 

FIG.  42. 


208 


PHYSICAL  CHEMISTRY 


a  a 


FIG.  43- 


During  the  time  indicated  by  cd,  the  temperature  remains 
constant.  On  further  cooling  a  regular  cooling  curve  is 
obtained,  as  represented  by  de. 

By  this  method  the  cooling  curves  of  solutions  over  the 
whole  range  of  concentrations  desired  may  be  obtained.  The 

temperature,  b,  at  which  these 
solutions  begin  to  solidify  has 
thus  been  determined.  So  if 
these  values  of  the  freezing 
points  are  plotted  on  a  temper- 
ature-concentration diagram 
against  their  respective  con- 
centrations and  the  points 
connected,  we  obtain  the 
curve  represented  by  a  dotted 
line,  the  freezing  or  solidification  curve.  If  on  this  diagram 
the  cooling  curves  be  superposed  so  that  the  freezing  points, 
6,  are  placed  on  the  freezing  curve  at  the  point  corresponding 
to  their  proper  concentration,  we  have  the  diagram  repre- 
sented by  Fig.  43. 

The  first  curve  at  the  left  is  the  cooling  curve  for  pure 
water,  and  we  have  the  usual  curve  for  a  pure  substance, 
with  the  break  occurring  at  b  when  it  begins  to  freeze,  and 
the  temperature  remaining  constant  until  the  liquid  has  all 
disappeared  (be),  when  the  cooling  again  becomes  regular, 
as  shown  by  the  section  ce.  It  will  be  noticed  that  the  cool- 
ing curve  for  a  solution  containing  23  per  cent  of  sodium 
chloride  is  exactly  like  this  and  is  analogous  to  the  cooling 
curve  of  a  pure  substance  as  shown  in  Fig.  41.  That  is,  at 
the  temperature  designated  /„  the  solidification  begins,  and 
the  temperature  remains  constant  until  the  whole  mass  has 
solidified.  This  takes  the  time  indicated  by  cd.  This 
freezing  point  is  different  from  the  freezing  point  of  any  of 
these  solutions  in  so  far  as  the  solidification  takes  place  at 
constant  temperature,  and  the  composition  of  the  solid 


SOLUTION  OF   SOLIDS   IN  LIQUIDS  209 

phase  separating  is  the  same  as  that  of  the  solution  from 
which  it  separates.  This  temperature  is  the  lowest  tem- 
perature at  which  any  solution  of  these  two  components  can 
exist.  It  is  also  the  lowest  melting  point  of  any  mixture  of 
the  two  components.  This  temperature  is  called  the 
eutectic  temperature ;  the  solid  which  separates  the  eutectic 
and  the  point  C,  Fig.  44,  is  called  the  eutectic  point.  When 
water  is  one  of  the  components,  this  point  is  also  termed  the 
cryohydric  point,  the  mixture  the  cryohydrate,  and  the  tem- 
perature the  cryohydric  temperature. 

For  all  solutions  in  which  the  concentration  of  the  sodium 
chloride  is  less  than  that  represented  by  the  point  C,  the 
solid  phase  separating  is  pure  water,  while  for  all  concentra- 
tions greater  than  C,  the  solid  phase  is  pure  sodium  chloride. 

The  curve  ACB,  Fig.  44,  represents  the  temperatures  at 
which  solutions  of  sodium  chloride  begin  to  solidify,  that  is, 
where  the  solid  phase  appears.  This  is  an  equilibrium  curve, 
and  since  it  is  not  a  continuous  curve,  but  composed  of  two 
branches,  it  must  represent  two 
different  conditions  of  equilibrium, 
that  is,  along  the  curve  AC  pure 
water  is  the  solid  phase  in  equi- 
librium with  the  solution,  and 
along  the  curve  CB  pure  NaCl 
is  the  solid  phase  in  equilibrium 

with  the  solution.     The  curve  A  C      ""freight  fcrcem  ** 

is  termed  the  Freezing  Curve  and  FlG  44 

the  curve  CB  the  Solubility  Curve, 
both  of  which  are  also  Solidification  or  Fusion  Curves.  The 
Eutectic  Point  may  also  be  defined  as  the  intersection 
of  two  fusion  curves  (of  a  freezing  curve  and  a  solubility 
curve) . 

That  the  time  required  for  the  solidification  of  these  dif- 
ferent solutions  is  not  the  same,  is  shown  by  the  different 
lengths  of  the  horizontal  sections  cd,  of  the  t-time  curves. 


210  PHYSICAL   CHEMISTRY 

This  indicates  that  there  are  different  quantities  of  the 
eutectic  formed,  and  consequently  the  times  required  for 
solidification  will  be  different,  and  we  have,  therefore,  an 
indication  of  the  relative  quantities  of  the  eutectic  separated 
upon  solidification  of  the  solutions  of  different  concentrations. 
The  area  above  the  curve,  ACB,  on  the  temperature- 
concentration  diagram,  Fig.  44,  represents  solutions  of 
sodium  chloride  in  water;  along  the  equilibrium  curve  AC 
solid  ice  separates;  along  the  equilibrium  curve  CB  solid 
NaCl,  while  at  the  intersection  of  these  two  curves  at  C  a 
mixture  of  ice  and  salt  separates,  consisting  of  22.43  Per 
cent  of  sodium  chloride.  Connecting  the  points  designated 
by  C,  we  obtain  the  line  DCE  parallel  to  the  concentration 
axis.  This  represents  the  lowest  limit  of  solidification  of 
all  mixtures  of  the  two  components.  In  the  area  between 
this  line  and  the  freezing  curve,  AC,  we  have  solution  and 
ice,  and  in  the  area  between  CB  and  CE  there  exist  solution 
and  salt,  while  below  DCE  we  have  solid  only  existing, 
which  consists  of  the  two  crystalline  species,  ice  and  salt. 

The  mutual  solubility  of  AgCl 
and  KC1  is  represented  on  the  tem- 
perature-concentration diagram,  Fig. 
45.  The  melting  point  of  KC1  is 
790°.  As  AgCl  is  added,  the  freezing 
point  is  lowered,  and  we  obtain  AC 
Tw)%  as  the  equilibrium  curve,  along  which 
KC1  is  the  solid  phase  separating, 
and  AC  is  a  fusion  curve.  Similarly, 
as  KC1  is  added  to  molten  AgCl,  the  melting  point  of  which  is 
451°,  represented  by  B,  the  freezing  point  is  lowered,  and  the 
curve  CB  represents  the  freezing  points  of  solutions  of  KC1  in 
AgCl.  The  solid  phase  separating  is  AgCl,  and  this-  is  in 
equilibrium  with  the  solution  along  the  fusion  curve  CB.  At 
the  intersection  C  of  the  two  fusion  curves,  both  KC1  and  AgCl 
separate  in  the  proportion  of  70  per  cent  of  AgCl  and  30 


SOLUTION  OF  SOLIDS  IN  LIQUIDS  211 

per  cent  of  KC1.  The  mixture  of  this  concentration  has  the 
lowest  fusion  point  of  all  mixtures  of  these  two  compounds  and 
is  therefore  the  eutectic,  and  the  eutectic  temperature  is  306°. 
The  fusion  curves  of  the  alloys  of  lead  and  antimony, 
which  show  the  existence  of  a  eutectic,  are  represented  on 
the  temperature-concentration  diagram  in  Fig.  46.  If  a 
melt  of  the  composition  represented  by 
m  be  selected  and  cooled,  pure  Pb  will 
separate  when  the  curve  AC  is  reached 
and  the  composition  of  the  liquid  will 


become  richer  in  Sb.     On  further  cool-       '£!* 

rT>  — 

ing,  the  fusion  curve  will  follow  the  line 

AC  until  sufficient  Pb  has  been  removed  to  bring  the  con- 
centration to  that  indicated  by  C,  the  eutectic,  when  the 
mass  will  solidify  without  change  of  temperature.  The 
same  is  true  of  mixtures  containing  more  Sb  than  indicated 
by  the  concentration  C.  When  these  molten  mixtures  are 
cooled,  the  pure  metal  Sb  separates  until  the  concentration 
C  is  reached,  when  the  mass  solidifies  like  a  pure  substance 
without  change  of  temperature.  It  is  evident  that  no  alloy 
of  these  two  metals  has  a  melting  point  lower  than  246°, 
the  eutectic  temperature,  which  is  represented  by  the  hori- 
zontal line  DCE  through  the  eutectic  point  C.  This  line 
also  represents  the  temperature  at  which  any  alloy  of  Pb-Sb 
would  begin  to  melt. 

The  concentration-temperature  diagram  is  divided  into 
the  following  fields  of  concentration  by  the  fusion  curves  and 
the  eutectic  horizontal : 
I    i.   Above  the  fusion  curve  ACB  is  the  liquid  or  melt. 

2.  In  area  ACD,  crystallized  Pb  is  in  equilibrium  with  the 
liquid. 

3.  In  area  BCE,  crystallized  Sb  is  in  equilibrium  with 
the  liquid. 

4.  In  the  field  below  DCE  the  homogeneous  crystalline 
mass,  composed  of  the  two  crystalline  solids  Pb  and  Sb, 


'  *  - . 
212  PHYSICAL  CHEMISTRY 

exists.  This  field  may  be  divided  into  two  areas  by  a  line 
parallel  to  the  temperature  axis  through  C.  These  have 
differences  in  structure,  recognized  microscopically.  Hence, 
the  eutectic  is  regarded  as  an  individual  structural  element 
in  all  metallurgical  investigations. 

In  many  cases  the  fusion  curves  do  not  show  a  marked 
eutectic  point  such  as  we  have  just  been  considering,  but  we 
have  a  fusion  curve  that  shows  that 
the  fusion  point  of  certain  mixtures 
lies  much  below  the  melting  point  of 
the  lower  melting  substance,  i.e.  they 
manifest  a  minimum  freezing  point. 
The  temperature-concentration  dia- 
gram for  mixtures  of  K^COs  and 


'<*>*        we,eh«%  100%    Na2CO3  employed  in  analytical  work 

K2C03  NnC03  r        J  J 

FIG.  47.  is  given  in  Fig.  47.      A  mixture  of 


and  Na2CO3  in  about  molecu- 
lar proportions  has  the  lowest  fusion  point,  about  700°,  and 
this  is  employed  in  fusions  in  preference  to  the  pure  compo- 
nents, as  the  reaction  with  the  refractory  substances  can  be 
carried  on  at  a  much  lower  temperature. 

In  the  preparation  of  explosive  mixtures  use  is  made  of 
this  same  principle  in  filling  shells.  It  is  desirable  to  intro- 
duce the  material  and  handle  it  in  liquid  condition.  Different 
explosives  are  mixed  so  as  to  produce  a  mixture  that  has  a 
low  melting  point,  thus  preventing  obnoxious  fumes,  loss  of 
material,  and  reducing  the  hazard  to  the  minimum.  In 
Table1  XXX  VI  are  given  a  few  explosives  with  their  melting 
points  and  also  the  melting  point  of  their  mixture. 

The  existence  of  eutectic  mixtures  is  a  very  common 
phenomenon.  Using  water  as  one  of  the  components,  the 
eutectic  (cryohydric)  point  for  a  great  many  substances  has 
been  determined,  and  in  Table  XXXVII  is  given  a  list  of 
some  of  these,  with  the  eutectic  (cryohydric)  temperature 
and  the  composition  of  the  eutectic  (cryohydrate)  , 


SOLUTION  OF   SOLIDS   IN   LIQUIDS 
TABLE  XXXVI 


213 


SUBSTANCE 

MELTING  POINT 

MELTING  POINT  OF 
MIXTURE 

Trinitrophenol                                   .    '.  l 

122 

Nitronaphthalene                        .     .     . 

6l 

49 

Trinitrophenol    .     . 
Dinitro  toluene                                  «     « 

122 
71 

47 

Trinitrophenol 

122 

Trinitrocresol     

107 

70 

TABLE  XXXVII 


SALT 

EUTECTIC 

(CRYOHYDRIC) 
TEMPERATURE 

PER  CENT  ANHY- 
DROUS SALT  IN  THE 
EUTECTIC 

(CRYOHYDRATEJ 

Sodium  bromide     
Sodium  iodide    
Sodium  chloride      
Sodium  nitrate 

-  28.0° 

-  31-5 
—  21.2 

—  18  * 

40-3 

39-0 
22.42 

-26  Q 

Potassium  iodide                   .... 

—  2T>  O 

C2  2 

Potassium  nitrate        * 
Potassium  bromide                          -I    . 

-3-0 
—  ii  ^ 

II.  2 
-IT  2 

Potassium  chloride                 .   •  .     . 

—  10  64. 

IQ  ^ 

Ammonium  sulphate        .     .     . 
Ammonium  chloride   

-  19-05 
—  1  6.00 

38.4 
19-5 

From  Fig.  44  it  is  apparent  that  at  the  eutectic  (cryohydric) 
temperature  for  the  system  NaCl  and  water,  the  four  phases — 
salt,  ice,  solution,  and  vapor — are  in  equilibrium.  We  have 
a  non variant  system.  If  we  add  heat  to  this  system,  we 
obtain  different  conditions,  depending  on  whether  ice  is  in 
excess  or  whether  salt  is  in  excess. 

i .  With  ice  in  excess,  on  heating,  the  ice  will  melt,  and  the 
salt  will  all  go  into  solution.  We  then  have  the  mono  variant 
system,  ice-solution-vapor. 


214  PHYSICAL   CHEMISTRY 

2.  With  salt  in  excess,  on  heating,  the  ice  will  melt,  the 
salt  will  dissolve,  and  as  more  heat  is  added  the  ice  will  all 
disappear  and  we  have  the  monovariant  system  salt-solution- 
vapor. 

Ice  and  salt  are  not  in  equilibrium  above  the  cryohydric 
temperature.  If  they  are  mixed  above  this  temperature  the 
ice  will  melt,  and  depending  upon  the  relative  quantities  of 
salt  and  ice,  we  shall  get  one  of  the  two  monovariant  systems, 
represented  by  CE  or  CF. 

When  ice  melts  heat  is  absorbed,  and  when  a  salt  dissolves 
heat  may  be  either  absorbed,  evolved,  or  neither  absorbed  nor 
evolved.  This  can  be  readily  ascertained  from  the  slope 
of  the  solubility  curve.  So  that  in  using  a  mixture  for  freez- 
ing purposes,  the  object  being  to  remove  heat  from  the 
substance  we  desire  to  cool,  it  is  evident  that  the  removal  of 
heat  is  going  to  be  accomplished  by  (a)  the  melting  of  the  ice 
and  (6)  the  solution  of  the  salt. 

If  the  salt  absorbs  heat,  then  the  two  factors  (a)  and  (6) 
are  going  to  work  together ;  but  if  the  salt  evolves  heat,  they 
will  oppose  each  other  ;  and  if  the  heat  of  solution  of  the  salt 
is  zero,  the  whole  cooling  effect  is  due  solely  to  the  melting 
of  the  ice.  Such  is  the  case  when  common  salt,  NaCl,  and 
ice  are  used. 

If  we  have  a  system  salt-ice-vapor  above  the  cryohydric 
temperature,  it  is  not  in  equilibrium  and  so  will  tend  to  pass 
into  a  state  of  stable  equilibrium.  The  temperature  will 
fall  until  (i)  one  or  both  of  the  solids  disappear  or  (2)  until 
the  cryohydric  temperature  is  reached.  This  is  the  lowest 
temperature  attainable  at  atmospheric  pressure  with  a  given 
freezing  mixture,  for  we  then  have  equilibrium  between  the 
solids  at  and  below  this  temperature.  The  temperature 
reached  in  the  laboratory  is  not  always  the  cryohydric  tem- 
perature, for  the  solution  that  is  being  continually  formed  has 
to  be  cooled  with  the  rest  of  the  system.  There  results  a 
temperature  at  which  the  heat  absorbed  by  the  solution 


SOLUTION   OF   SOLIDS   IN   LIQUIDS  215 

being  formed,  in  unit  time,  is  just  sufficient  to  keep  the  mass 
of  solution  present  at  a  constant  temperature.  Attaining 
the  minimum  temperature,  then,  depends  on  (i)  the  initial 
temperature,  (2)  the  rate  of  radiation,  (3)  quantities  of  salt 
and  ice  used,  and  (4)  the  thoroughness  of  the  mixture, 
since  the  speed  of  reaction  is  proportional  to  the  surfaces  of 
the  solids.  When  the  ice  is  in  large  pieces,  less  heat  will  be 
absorbed  in  unit  time.  Therefore,  the  equilibrium  will  be 
reached  at  a  higher  temperature  than  if  the  pieces  are  small. 
In  order  to  obtain  a  low  temperature  by  means  of  a  freezing 
mixture  the  following  precautions  should  be  observed : 

1.  Select  a  mixture  with  a  low  cryohydric  temperature. 

2.  Select  a  mixture  such  that  the  heat  absorbed  per  gram 
of  solution  formed  is  as  great  as  possible.     This  is  realized  if 
the  solubility  increases  rapidly  with  the  temperature.     (NaCl 
is  not  ideal,  as  heat  absorbed  is  nearly  zero,  hence  the  heat 
absorbed  is  due  practically  to  the  melting  of  the  ice.) 

3.  Take  substances  in  proportion  indicated  by  the  cryohy- 
drate. 

4.  Remove  solution  as  fast  as  formed. 

5.  Use  fine  material  to  increase  speed  of  reaction,  thus 
producing  maximum  absorption  in  unit  time. 


CHAPTER  XX 
SOLUTION  OF  SOLIDS  IN   LIQUIDS  — m 

SOLVENT  AND   SOLUTE   CRYSTALLIZE  IN  ACCORDANCE  WITH 
THE  LAWS  OF  DEFINITE  AND  MULTIPLE  PROPORTIONS 

TYPE  II 

MANY  substances  on  crystallizing  from  aqueous  solutions 
are  found  to  contain  a  considerable  amount  of  the  solvent, 
which  is  always  in  a  definite  ratio  to  the  solute  or  some 
multiple  of  this  ratio.  The  solute  is  said  to  crystallize  with 
water  of  crystallization,  e.g.  CuSC>4  •  5  H2O  ;  Na2SO4  •  10  H2O, 
etc.  Other  solvents  than  water  act  in  a  similar  manner, 
and  we  may  have  alcohol  of  crystallization,  benzene,  acetone, 
etc.  The  compounds  containing  water  of  crystallization 
are  known  as  hydrates  and  have  been  very  extensively  studied, 
while  those  in  which  other  liquids  appear  as  the  solvent 
have  also  been  studied.  It  is  possible  for  us  to  take  up  the 
consideration  of  only  a  few  of  the  hydrates. 

Sodium  Sulphate  and  Water.  —  From  the  solubility  de- 
terminations of  sodium  sulphate  in  water,  the  data  of  which 
are  represented  diagrammatically  on  the  concentration-tem- 
perature diagram,  Fig.  48,  it  is  apparent  that  the  curves 
represent  the  equilibrium  between  different  solid  phases  and 
the  solution. 

The  abscissas  are  the  per  cent  of  sodium  sulphate,  the  or- 
dinates  the  temperature,  and  the  system  is  supposed  to  be 
under  its  own  pressure. 

Starting  with  water  at  zero  degrees,  the  freezing  points  of 
the  solutions  of  increasing  concentration  are  represented 

216 


SOLUTION  OF   SOLIDS   IN  LIQUIDS  217 

by  the  curve  A  B,  familiarly  known  as  the  freezing-point 
curve.  At  B,  the  cryohydric  point,  the  hydrate 
Na2SO4  •  ioH2O  begins  to  crystallize  out,  and  we  have  the 
inversion  point  at  —1.2°  and  a  concentration  of  about  40 
grams  per  100  grams  of  water.  The  curve  BC  represents 
.the  solubility  curve  for  the  decahydrate  and  is  an  equilib- 
rium curve  between  the  solid  and  the  solution.  On  heating 
there  is  a  decrease  in  the  solubility,  as  is  represented  by  the 
curve  CD,  which  is  an  equilibrium  curve  between  the  anhy- 
drous solid  and  the  solution.  The  intersection  of  these  two 
solubility  curves  at  C  indicates  an- 
other transition  point,  and  we  have 
the  two  solid  phases  in  equilibrium 
with  the  solution  and  vapor.  The 
temperature  of  this  transition  point 
is  32.5°  (Richards,  32.379°  hydrogen 
thermometer,  32.482°  mercury  ther- 
mometer) at  a  concentration  of  49.8 
grams.  Hence,  above  this  tempera- 
ture the  solid  anhydrous  salt  is  in  equilibrium  with  the 
solution,  and  below,  the  hydrated  salt  with  ten  molecules 
of  water  of  crystallization.  The  curve  BCD  is  then  not 
a  continuous  curve,  but  the  solubility  curve  shows  a  break 
or  discontinuity  in  direction,  which  is  characteristic  of  the 
sulphates  and  indicates  that  entirely  different  phases  are 
in  equilibrium  along  the  respective  curves.  The  curve  BC 
has  not  been  realized  very  far  beyond  the  inversion  tem- 
perature C. 

There  is  one  other  hydrate  known,  the  heptahydrate, 
which  can  be  very  readily  obtained  in  the  presence  of  alcohol, 
but  which  also  separates  out  of  a  solution  of  sodium  sul- 
phate which  has  been  saturated  at  about  34°  and  allowed  to 
cool  below  17°,  having  it  protected  very  carefully.  The  com- 
position of  these  crystals  which  separate  is  Na2SO4  •  7  H2O. 
The  solubility  curve  for  this  solid  is  represented  by  EB', 


" 

2l8  PHYSICAL  CHEMISTRY 

and  its  intersection  with  DC  continued  in  the  vicinity  of 
25°  represents  a  labile  nonvariant  system  and  of  course 
unstable  with  respect  to  Na2SO4  •  ioH2O. 

We  stated  that  the  solubility  curve  of  the  decahydrate 
had  been  carried  out  a  little  ways  beyond  the  transition 
point.  Above  this  point  the  solubility  of  the  decahydrate 
is  greater  than  that  of  the  anhydrous  salt,  and  so  a  solution 
which  is  saturated  with  the  decahydrate  would  be  super- 
saturated with  respect  to  the  anhydrous  salt.  Likewise, 
if  we  have  a  concentration  and  the  temperature  of  a  solu- 
tion as  represented  by  the  point  N,  and  this  be  cooled  in  a 
closed  vessel,  the  changing  state  of  the  system  will  be  rep- 
resented by  the  vertical  line  TV  N' .  At  N'  the  solid  phase 
decahydrate  should  appear.  If,  however,  the  solution  be 
cooled  carefully,  it  may  be  possible  to  get  the  temperature 
much  below  that  indicated  by  N'  and  prolong  the  line  con- 
siderably. The  solution  contains  very  much  more  salt 
than  a  saturated  solution  contains  and  is  said  to  be  super- 
saturated, for  if  the  solid  phase  of  Na2SO4  •  10  H2O  be  brought 
in  contact  with  the  solution,  the  amount  of  the  salt  in  ex- 
cess of  that  contained  in  a  saturated  solution  at  that  tem- 
perature will  be  separated  out.  Hence,  our  definition  of  a 
saturated  solution  must  contain  the  statement  as  to  the 
temperature  of  the  solution  and  the  solid  phase  with  which 
it  is  in  equilibrium.  It  might  be  stated,  however,  that  any 
substance  which  is  isomorphous  with  the  solid  phase  will  also 
produce  the  precipitation. 

This  phenomenon  of  supersaturation  is  not  confined  to 
aqueous  solutions,  but  it  may  be  stated  in  general  that  those 
salts  that  separate  out  with  water  of  crystallization  form 
supersaturated  solutions  much  more  readily  than  those  that 
separate  in  the  anhydrous  form.  This  is  by  no  means  uni- 
versal, for  many  substances  which  separate  in  the  anhydrous 
state  form  supersaturated  solutions  very  readily.  This  is 
true  for  silver  nitrate  and  sodium  chlorate  in  aqueous  solu- 


SOLUTION  OF  SOLIDS   IN  LIQUIDS  219 

tions,  while  in  the  case  of  organic  solvents  this  is  very  com- 
mon. It  is  generally  held  that  those  salts  that  separate 
with  water  of  crystallization  form  large  crystals  and  form 
most  easily  on  crystals  already  present,  while  salts  that  form 
supersaturated  solutions  with  difficulty  crystallize  spon- 
taneously in  very  small  crystals. 

Pressure-Temperature  Diagram  of  Sodium  Sulphate  and 
Water.  —  The  curves  A B,  AC,  and  AM,  Fig.  49,  represent 
the  system  for  pure  water.  We  saw  that  upon  adding  a 
solid  solute  to  water  the  vapor  pressure  of  the  system  was 
lowered.  If  Na2SO4  is  added  to  water,  p 
the  resulting  solution  will  have  a  lower 
vapor  pressure  than  the  pure  solvent 
under  the  same  conditions  of  tem- 
perature. We  shall  then  have  the 
following  systems : 

Curve    CD,    mono  variant    system  — 


Hydrate-solution-vapor.  <IG'  49' 

Curve  CA ,  monovariant  system  —  Ice-solution-vapor. 

Curve  C  K,  monovariant  system  —  Hydrate-solution-ice. 

Curve  CH,  monovariant  system  —  Hydrate-ice-vapor. 

Point  C,  cryohydric  point,  non variant  system  —  Hy- 
drate-ice-solution-vapor. 

If  under  the  conditions  represented  by  C,  the  system  is 
heated  and  the  volume  kept  constant,  the  ice  will  disappear 
first  and  we  shall  have  the  system  —  solution-hydrate- 
vapor,  which  will  increase  in  temperature  with  increased 
pressure,  and  the  curve  CD  will  represent  the  equilibrium  of 
the  system.  At  the  point  D  the  solid  anhydrous  phase  ap- 
pears, and  there  results  the  non  variant  system  —  anhydrous 
salt-hydrate-solution-vapor.  This  point  D  represents  the 
inversion  point  and  is  the  intersection  of  four  curves  DE, 
DF,  DC,  and  DG  at  the  temperature  32.5°  and  a  pressure 
30.8  mm.  of  mercury,  representing  the  four  possible  mono- 
variant  systems : 


220 


PHYSICAL  CHEMISTRY 


DE  —  Anhydrous  salt-solution-vapor. 

DF  —  Hydrate-anhydrous  salt-solution. 

DC  —  Hydrate-solution-vapor. 

DG  —  Anhydrous  salt-solution-vapor. 

The  vapor  pressure  curve  for  anhydrous  salt  DG  is  below 
that  for  the  hydrate  DC,  but  the  stable  system  below  32.5°, 
D,  is  the  hydrate-solution-vapor,  and  the  labile  system  is 
anhydrous  salt -solution- vapor.  But  this  is  the  reverse  of 
what  we  considered  under  the  sulphur  system,  where  we 
saw  that  the  stable  system  was  that  one  which  had  the 
lower  vapor  "pressure.  The  more  stable  system  is  the  one 
with  the  lesser  concentration  and  therefore  greater  vapor 
pressure.  This  is  a  general  condition,  as  there  are  two 
forces  acting :  (i)  the  tendency  of  the  vapor  to  distill  from 
the  higher  to  the  lower  pressure  and  (2)  the  tendency  of  the 
solute  to  precipitate  from  the  more  concentrated  solutions. 
The  latter  is  the  stronger,  but  either  would  bring  about 
equilibrium.  This  condition  depends  upon  the  fact  that 
the  less  stable  form  is  the  more  soluble,  and  as  the  lowering 
of  the  vapor  pressure  is  proportional  to  the  concentration, 
the  result  is  a  much  lower  vapor  pressure  for  the  labile  solu- 
tions (Bancroft's  Phase  Rule). 

Solubility  Curves  of  Hydrates  Which  Do  Not  Have  a 
Definite  Melting  Point.  —  The  following  diagrams,  Figs.  50, 
51,  and  52,  illustrate  the  types  of  solubility  curves  obtained 
for  salts  that  crystallize  with  water  of  crystallization. 


10%  30%  50% 

FIG.  50. 


%  Nal  80* 

FIG.  51. 


%  CulNOjj), 

FIG.  52. 


SOLUTION  OF   SOLIDS   IN  LIQUIDS  221 

Each  solubility  curve  is  made  up  of  a  number  of  individual 
curves,  each  of  which  represents  the  equilibrium  between 
some  specific  hydrate  and  solution,  and  there  will  be  as 
many  different  solid  phases  separating  as  there  are  seg- 
ments. Hence,  in  determining  the  solubility  of  a  substance 
it  is  necessary  to  know  the  composition  of  the  solid  phase  in 
equilibrium  with  the  solution  as  well  as  the  temperature  at 
which  this  equilibrium  is  established.  To  establish  thor- 
oughly the  point  of  equilibrium  it  is  best  to  approach  it  from 
both  a  higher  and  a  lower  temperature,  or  by  establishing 
the  rate  at  which  it  is  attained.  A  saturated  solution  is  a 
solution  in  equilibrium  with  the  solid  phase  (i.e.  with  the  pure 
solute)  at  a  specified  temperature.  In  these  cases  the  pure 
solutes  are  the  hydrates  and  the  anhydrous  salt. 

Solubility  Curves  of  Hydrates,  Some  of  Which  May  Have 
a  Definite  Melting  Point.  —  The  following  solubility  curves, 
Figs.  53,  54,  and  55,  represent  the  equilibrium  curves  of 
substances,  some  of  the  hydrates  of  which  melt  without 
change  of  temperature  and  form  a  liquid  of  the  same  com- 
position as  that  of  the  crystalline  solid  hydrate. 

It  will  be  noticed  that  the  curves  starting  from  the  left 
of  the  figure  represent  first  the  lowering  of  the  freezing  point 
of  water  as  the  concentration  of  the  solute  is  increased. 
This  is  usually  designated  a  freezing-point  curve,  and  it  is 
a  cooling  curve  for  the  solvent  which  separates  along  this 
curve,  as  solutions  of  concentrations  up  to  that  represented 
by  B  are  cooled.  It  also  represents  the  temperatures  at 
which  mixtures  of  these  concentrations,  when  in  the  solid 
state,  will  have  to  be  heated  before  they  begin  to  melt; 
they  may  also  be  termed  fusion  curves.  We  reach  a  mini- 
mum value  for  the  temperature  at  which  the  mixture  of  the 
compounds  can  exist  in  the  liquid  state.  This  temperature 
is  the  eutectic  temperature,  or  when  water  is  the  solvent, 
it  is  termed  the  cryohydric  temperature. 

The  curve  BCD  is  termed  the  solubility  curve.     This  is 


Weight  7. 


- 

222  PHYSICAL   CHEMISTRY 

an  equilibrium  curve,  for  all  along  this  curve  the  same  solid 
phase  (a  hydrate)  is  in  equilibrium  with  the  solutions  of 
various   concentrations.     The   temperature   at   which   this 
hydrate  is  in  equilibrium  with  the  saturated  solution  in- 
creases with  increased  concentration  until  a  maximum  value, 
C,  is  reached,  when  the  solid  hydrate  is  of  the  same  concen- 
tration as  that  of  the  solution  from 
which  it  separates.     In  other  words, 
if  we  had  a  solution  of  this  specific 
concentration  and  cooled  it,  at  the 
temperature  represented  by  this  maxi- 
mum value  the  whole  solution  would 
solidify  without  change  in  tempera- 
ture,  or  if  we  had  a  solid  hydrate  of 
FlG  S3  this  concentration,  it  would  melt  at 

this  temperature  without  change  in 

temperature,  i.e.  it  has  a  constant  melting  point,  and  the 
solution  has  a  constant  freezing  point.  These  are  charac- 
teristics of  pure  chemical  compounds,  and  therefore  we 
conclude  that  such  points  as  C  represent  definite  chemical 
compounds,  which  in  these  cases  are  termed  hydrates. 

The  remainder  of  the  curve  CD  shows  a  decrease  in  the 
temperature  at  which  this  solid  hydrate  is  in  equilibrium 
with  solutions  of  increasing  concentration.  This  decrease 
continues  until  the  point  D  is  reached,  where  our  solubility 
curve  is  intersected  by  another  so-called  solubility  curve, 
DBF,  along  which  another  solid  phase  of  a  different  hy- 
drate separates  and  is  in  equilibrium  with  a  series  of  still 
more  concentrated  solutions.  It  will  be  noticed  that  this 
portion  of  the  curve  is  practically  a  repetition  of  what  we 
have  just  explained :  the  point  E  represents  the  maximum 
temperature  at  which  this  solid  hydrate  is  in  equilibrium 
with  the  solution  and  is  the  melting  point  of  the  hydrate, 
and  melting  points  of  this  character  are  termed  congruent 
melting  points. 


SOLUTION   OF   SOLIDS   IN  LIQUIDS  223 

The  retroflex  portion  of  the  curve  EF,  similar  to  CD,  is 
really  similar  to  A B,  the  freezing-point  curve,  for  in  all  of 
these  cases  we  have  a  case  of  the  lowering  of  the  freezing 
point  of  the  solute  by  the  addition  of  a  second  component. 
This  second  component  in  all  cases  is  the  anhydrous  salt, 
but  the  solvent  in  the  first  case  is  pure  water,  the  freezing 
point  of  which  is  A  ;  in  the  second  case  the  solve  at  is  the 
hydrate  of  the  composition  represented  by  C,  the  freezing 
point  of  which  is  the  temperature  corresponding  to  C\ 
while  the  solvent  in  the  third  case  is  the  hydrate  of  the  com- 
position E,  the  freezing  point  corresponding  to  the  tem- 
perature E.  It  is  then  apparent  that  these  curves,  which 
we  term  solubility  curves  (portions  of  them  at  least),  are 
readily  recognized  as  freezing-point  curves  or  fusion  curves. 
It  is  also  apparent  that  if  these  values  were  plotted  with 
the  two  components  interchanged,  the  portions  of  the  curves 
we  have  been  designating  solubility  curves  become  the  por- 
tions recognized  as  the  freezing-point  curves  and  the  freez- 
ing-point curves  become  the  solubility  curves.  We  are, 
therefore,  justified  in  using  the  terms  fusion  curves,  solu- 
bility curves,  and  freezing-point  curves  as  synonymous, 
and  subsequently  we  shall  do  so.  It  is  evident  that  the  in- 
tersection of  a  fusion  and  a  solubility  curve  is  the  eutectic 
or  cryohydric  point,  or  this  point  could  be  defined  as  the 
point  of  intersection  of  two  fusion  curves. 

If  at  any  temperatures  between  C  and  D  a  horizontal  line 
be  drawn,  it  will  intersect  the  solubility  curve  BCD  in  two 
points,  which  indicates  that  for  the  same  temperatures  there 
are  two  solubilities  of  the  hydrate  of  the  composition  rep- 
resented by  C.  In  the  weaker  solution  we  have  a  hydrate 
separating  which  is  richer  in  the  solute  component  than  the 
solution,  while  in  the  other  case  the  concentration  of  the 
solution  is  richer  than  the  hydrate  in  the  solute  component. 
The  hydrate  can  exist  in  equilibrium  with  two  solutions  of 
very  different  concentrations  at  the  same  temperature. 


224 


PHYSICAL   CHEMISTRY 


In  the  diagram,  Fig.  54,  representing  the  solubility  curve 
of  FeCl3  in  water,  let  us  draw  the  line  XY  representing  a 
temperature  of  about  31.2°.  If  a  solution  of  ferric  chloride 
is  evaporated  at  this  constant  temper- 
ature, the  concentration  will  increase  until 
the  solubility  curve  BC  is  intersected, 
when  FeCl3  •  12  H2O  will  crystallize  out. 
This  crystallization  will  continue  until  all 
the  solution  will  have  disappeared.  Lique- 
faction occurs  again  where  CD  is  intersected 
and  at  the  concentration  on  DF  above  D 
solidification  again  occurs.  On  further 
evaporation  liquefaction  again  occurs  and 
at  the  intersection  of  FG  it  again  solidifies 

407o  80% 

t  %  Fe4ci«       an(j  remains  solid.     Hence  we  have  suc- 
cessively solution ;   solidification  to  dode- 
cahydrate ;    liquefaction  ;    solidification   to    heptahydrate ; 
liquefaction ;  solidification  to  pentahydrate. 

In  the  case  of  the  system  H2O-SO3,  Fig.  55,  we  have  a 
marked  example  of  the  formation  of 
hydrates.     Here  we  have  five  as  rep- 
resented  by   the    congruent   melting 
points  C,  E,  H,  J,  and  L. 

This  type  of  solubility  curve,  which 
exhibits  a  congruent  melting  point, 
is  common  in  aqueous  solutions,  and 
when  other  substances  are  employed 
as  the  solvent,  as  mixtures  of  organic 
substances  and  in  alloys,  we  find 
it  a  very  common  type  of  solubility 
curve.  This  fact  in  the  latter  cases 
is  used  as  a  basis  for  the  estab- 


H20+2S03=H2S207 
H2O+SO3  =H2SO4 
2H2O+SO3  =I12SO4+H2O 


fflP 


FIG.  55- 


lishment    of    the    existence    of    chemical    compounds. 

Vapor    Pressure    of    Hydrates.  —  The    dehydration    of 
crystalline   hydrates   is   analogous   to   the   dissociation   of 


SOLUTION  OF  SOLIDS   IN  LIQUIDS 


225 


other  substances  such  as  ammonium  chloride,  which  on  dis- 
sociation gives  NH4C1  ^  NH3  +  HC1.  Similarly  we  have 
Cu(NO3)2  •  6  H20  ^  Cu(NO3)2  •  3  H2O  +  3  H2O  ;  but  as  we 
have  a  two-component  system,  salt-water,  in  three  phases, 
we  have  a  mono  variant  system,  and  at  each  specified  tem- 
perature there  will  be  a  certain  definite  corresponding  vapor 
pressure  which  is  independent  of  the  masses  of  the  phases 
present. 

Hydrated  salts  give  off  their  water  of  crystallization  as 
vapor  in  vacua.  This  is  also  true  when  the  substance  is 
heated  at  other  pressures,  and  for  a  definite  temperature 
there  is  a  certain  pressure  of  the  vapor  which  is  independent 
of  the  water  given  off  as  vapor.  This  law  has  been  very 
thoroughly  established,  and  the  vapor  pressures  of  many 
hydrated  salts  have  been  measured.  The  vapor  pressure  in 
millimeters  of  mercury  of  a  number  of  hydrates  is  given  in 
Table  XXXVIII,  which  shows  the  variation  of  the  pressure 
with  the  temperature. 

TABLE  XXXVIII 


SALT 

TEMPERATURE 

PRESSURE  MM.  He. 

Na-HPO4  •  10  H2O                           ... 

17  28° 

IO  S^I 

Na2HPO4  •  10  H2O  

27 

21.575 

ZnSO4  •  7  H2O     ..  '  . 
ZnSO4-7H2O                                   .     . 

18. 

2Q  Q5 

8.406 
22  ^8q 

SrQ2-6H2O  . 

10  7 

5.6l 

SrCl2-6H2O 

•57  cc 

IQ  86 

BaCl2  •  2  H2O                               .''  .    . 

18  25 

2.Q7 

BaCl2  •  2  H2O      

43.4.C 

21.117 

The  diagrammatic  representation  of  the  different  hydrates 
of  copper  sulphate  is  given  in  Fig.  56. 

The  vapor  pressure  curves  are : 
BA  for  pure  water. 


226 


PHYSICAL  CHEMISTRY 


CE  for  saturated  solutions  in  equilibrium  with  the  penta- 

hydrate. 

Os  dissociation  curve  for  CuS04  •  5  H2O  ;  CuSO4-3  H2O+ 2  H2O 
03  dissociation  curve  for  CuSO4  •  3  H2O  ;  CuSO4  •  H2O+2  H2O 
Oi  dissociation  curve  for  CuSO4  •  H2O  ;  CuSO4  +  H2O 

If  at  some  arbitrarily  selected 
temperature,  as  indicated  at  k, 
water  vapor  be  admitted  to  the 
anhydrous  CuSO4,  the  vapor  pres- 
sure will  increase.  By  the  contin- 
uous addition  of  water  vapor  the 
vapor  pressure  will  continue  to  in- 
crease, and  at  various  pressures  we 
should  have  the  vapor  in  equilib- 
rium with  the  different  hydrates 
represented  by  the  intersection  of  the  vertical  line  from 
k  intersecting  the  vapor  pressure  curves  at  the  points 
j,  i,  h,  g,  and  /  respectively,  when  we  should  obtain  an 
infinitely  dilute  solution  the  vapor  pressure  of  which  would 
be  practically  that  of  pure  water,  represented  by  the 
intersection  /. 

Pareau  measured  the  values  of  the  vapor  pressure  of 
hydrates  of  CuSO4  by  withdrawing  the  vapor  gradually 
and  establishing  points  of  equilibrium  of  the  lower  hydrates 
thus  formed.  The  data  in  Table  XXXIX  were  obtained  by 
him  at  50°. 

TABLE  XXXIX 


FIG.  56. 


PRESSURE 


CuSO4  •  4  5  H2O 

46  3  mm 

CuS04-3.5H20  
CuSO4-2.5H2O  
CuSO4  •  i  5  H2O  ...  

47.1  mm. 
29.9  mm. 
29.7  mm. 

CuSO4-o.5H2O  ^.  . 

4.4  mm. 

SOLUTION  OF  SOLIDS  IN  LIQUIDS  227 

For  compositions  between  CuSO4  •  5  H2O  and  CuS04-  3  H2O 
the  pressure  remains  practically  constant  at  47  mm. ;  it  then 
drops  to  30  mm.,  at  which  pressure  it  stays  until  there  re- 
mains only  one  molecule  of  water  of  crystallization,  when 
the  pressure  falls  to  4.4  mm.,  at  which  it  remains  until  the 
salt  is  completely  dehydrated  and  we  have  the  anhydrous 
salt. 

This  may  be  represented  on  a  pressure-concentration 
diagram  at  50°,  as  is  shown  in  Fig.  57.  The  vapor  pressure 
of  pure  water  at  50°  is  represented  by  /,  and  as  the  CuSO4 
is  added  the  vapor  pressure  changes  as 
represented  by  the  line  /g,  when  a 
saturated  solution  is  reached,  as  shown 
by  curve  CE  in  Fig.  56.  Now  the 
vapor  pressure  remains  constant  until 
sufficient  anhydrous  salt  has  been  added 
to  convert  the  CuSO4  •  5  H2O  all  into 
CuSO4  •  3  H2O,  and  then  the  vapor  ««»  ESQ. 

pressure  drops  suddenly  to  47  mm.  <IG>  S7' 

If  we  were  to  start  with  the  anhydrous  salt  CuSO4  and 
add  water  vapor,  the  vapor  pressure  would  increase  until 
we  reach  point  j,  Fig.  57,  when  the  monohydrate  will  be 
formed,  and  we  shall  have  the  monovariant  system  CuS04- 
CuSO4  •  H2O-vapor  at  constant  temperature  and  constant 
pressure  (4.4  mm.).  By  continued  addition  of  vapor  there 
will  be  a  continued  formation  of  the  monohydrate  from  the 
anhydrous  CuSO4  until  it  has  all  disappeared,  when  we  have 
a  divariant  system  represented  by  line  ji  with  increase  of 
pressure  until  i  is  reached,  which  represents  the  formation 
of  the  trihydrate,  when  we  have  a  new  monovariant  system 
CuS04  •  H2O-CuSO4  •  3  H2O-vapor.  The  pressure  on  this 
system  will  remain  constant  (30  mm.)  until  there  has  been 
added  enough  vapor,  to  convert  all  of  the  CuSO4  •  H2O  into 
CuSO4  •  3  H2O.  As  soon  as  this  occurs  we  have  a  divariant 
system,  the  pressure  on  which  changes  as  represented  by 


228  PHYSICAL   CHEMISTRY 

ih  until  h  is  reached,  and  we  have  the  new  mono  variant 
system  CuSO4  •  5  H2O-CuSO4  •  3  H2O-vapor,  when  the  pres- 
sure (47  mm.)  will  remain  constant  until  all  of  the  trihydrate 
has  disappeared,  when  we  have  a  new  di variant  system 
CuSO4  •  5  H2O-vapor.  The  pentahydrate,  like  the  other  hy- 
drates, can  exist  with  water  vapor  at  different  pressures, 
and  the  area  sOCE  represents  the  area  in  which  this  di- 
variant  system  may  exist.  So  that  if  the  vapor  pressure  at 
this  temperature  is  increased,  at  g  the  vapor  will  begin  to 
condense,  and  we  shall  have  introduced  the  new  phase — 
solution.  The  curve  CE  then  represents  the  equilibrium 
between  CuSO4  •  5  H2O-solution-vapor  and  is  the  vapor  pres- 
sure curve  of  saturated  solutions. 

Data  such  as  represented  for  copper  sulphate  and  its 
hydrates  enable  us  to  determine  the  relation  between  the 
vapor  pressure  of  water  in  the  atmosphere  under  ordinary 
conditions  and  that  of  the  hydrates.  So  that  a  particular 
hydrate,  such  as  the  pentahydrate  CuSO4  •  5  H2O,  with  a 
vapor  pressure  represented  by  curve  O$,  Fig.  56,  begins  to  lose 
water  of  crystallization  if  it  is  brought  into  an  atmosphere 
in  which  the  vapor  pressure  is  less  than  the  amount  repre- 
sented by  05  ;  it  will  take  on  water  if  the  vapor  pressure  in 
the  atmosphere  is  greater  than  the  pressure  represented  by 
05.  This  process  of  crystalline  hydrates  losing  water  of 
crystallization  under  atmospheric  conditions  is  designated 
efflorescence,  and  the  process  of  taking  on  water  is  designated 
deliquescence.  This  principle  is  made  use  of  in  the  processes 
of  desiccation,  and  the  particular  substances  employed, 
such  as  H2SO4,  CaCl2,  etc.,  have  low  vapor  pressures  and 
become  hydrated  by  the  absorption  of  the  water  from  the 
substance  to  be  dried. 


CHAPTER  XXI 
SOLUTION   OF   SOLIDS  IN  LIQUIDS  — IV 

SOLVENT  AND  SOLUTE  CRYSTALLIZE  TO  FORM  SOLID  SOLU- 
TIONS OR  MIXED  CRYSTALS 

TYPE  III 

IN  the  examples  of  the  freezing  point  of  mixtures  we  have 
assumed  that  the  solid  phases  that  separated  were  the  pure 
substances  along  their  respective  solubility  curves,  and  at 
only  one  point  —  the  eutectic  point  —  did  we  have  the  two 
solids  separating  together.  This  is,  however,  only  a  special 
case,  for  in  a  large  number  of  binary  mixtures  the  solid  phase 
separating  along  the  fusion  curve  consists  of  a  mixture  of  the 
two  components  in  proportions  varying  within  certain  limits. 
This,  as  we  recall,  is  our  definition  of  a  solution,  and  these 
solid  phases  that  separate  were  termed  solid  solutions  by 
van't  Hoff.  They  are  generally  termed  mixed  crystals  or 
isomorpkous  mixtures. 

It  will  be  recalled  that  the  addition  of  a  solute  lowers  the 
freezing  point  of  the  solvent,  and  the  greater  the  concentra- 
tion the  greater  the  lowering  until  we  reach  the  maximum 
solubility  in  saturated  solutions,  when  we  have  the  eutectic 
temperature  reached. 

Let  BC,  Fig.  58,  be  the  vapor  pressure  curve  and  BD  the 
sublimation  curve  for  the  pure  solvent  water.  On  addition 
of  a  solute  the  vapor  pressure  is  lowered,  and  as  the  concen- 
tration is  increased  the  vapor  pressure  curve  takes  the  succes- 

229 


230 


PHYSICAL  CHEMISTRY 


FIG 


sive  positions  indicated  by  the  dotted  lines.  These,  continued 
until  they  intersect  the  curve  BD,  give  the  triple  point  for 
the  successive  solutions,  with  the  cor- 
responding lowering  of  the  freezing 
temperature. 

Our  explicit  assumption  in  this 
case  is  that  the  vapor  pressure  of  the 
solid  phase  as  represented  by  the 
sublimation  curve  is  that  of  the  pure 
solvent,  i.e.  that  the  solid  phase  that 
separates  is  pure  solvent,  and  BD  is  its  sublimation 
curve.  Now,  if  the  solute  and  solvent  separate  together, 
the  vapor  pressure  of  this  solid  phase  will  be  different  from 
that  of  the  pure  solvent  as  represented  by  the  freezing 
curves. 

We  may  represent  this  in  Fig.  59,  where  the  vapor  pressure 
of  the  solid  phase  separating  varies  with  the  increase  of 
solute,  and  we  have  also  the  vapor 
pressure  curves  of  these  various  solid 
solutions  represented  by  a,  b,  c. 
The  values  of  these  vapor  pressures 
are  higher  than  they  would  be  were  the 
solid  that  separates  pure  solvent.  It 
is  evident  that  the  freezing  point  (rep- 
resented by  the  intersection  of  a,  a' ; 


FIG.  59. 


b,  bf ;  c,  c')  is  raised,  and  it  may  be  higher  than  that  of  the 
pure  solvent.  We  thus  have  mixtures  separating  which  have 
many  of  the  properties  of  ordinary  liquid  solutions,  although 
they  are  in  the  solid  state.  These  are  called  solid  solutions 
or  mixed  crystals,  and  are  also  termed  isomorphous  mixtures. 
If,  however,  a  solution  of  two  metals,  M  and  A/",  which  are 
miscible  at  all  temperatures,  be  allowed  to  cool,  we  have  a 
somewhat  different  cooling  curve,  as  illustrated  in  Fig.  60. 
The  part  of  the  cooling  curve,  AB,  is  regular,  but  at 
the  temperature  tB  the  solid  separating  out  is  a  mixture 


SOLUTION  OF  SOLIDS  IN  LIQUIDS 


23I 


of  M  and  N,  richer  in  M  than  the  mother  liquor.  The 
temperature  at  which  more  crystals  can  be  separated  from 
it  becomes  lower  and  lower,  and  this  may  be  represented  by 
BC.  When  the  temperature  /cis  reached,  the  whole  mass 
solidifies,  and  the  cooling  curve  CD  then 
represents  the  regular  cooling  of  the 
solid  mass. 

Fusibility  Curves  of  Binary  Alloys.  — 
If,  in  the  manner  which  was  described  on 
page  207,  cooling  curves  be  obtained  for 
alloys  of  different  percentage  composi- 
tion and  these  results  plotted  on  a 
temperature-concentration  diagram,  we 
have  a  means  of  obtaining  the  fusibility  curves  or  equilib- 
rium diagram  for  all  possible  mixtures  of  these  two  metals 
for  all  ranges  of  temperature.  Figure  61  illustrates  the 
fusibility  curves  so  constructed.  Let  M  and  N  represent 
respectively  the  melting  points  of  the  two  metals  M  and  N, 
then  the  horizontal  axis,  represents  all 
possible  mixtures  of  the  metals  M  and  N. 
The  curve  MBBX-N  represents  the 
points  of  initial  solidification  and  is 
designated  the  liquidus  curve.  Now 
by  connecting  the  points  MCCX-N, 
we  get  an  equilibrium  curve  which 
represents  all  temperatures  at  which  all 
mixtures  of  the  two  metals  M  and  N 
completely  solidify,  and  this  is  designated  the  solidus  curve. 
Cooling  Curves.  —  By  means  of  the  thermoelectric  py- 
rometer, temperature  measurements  can  be  readily  made  and 
data  obtained  for  determining  the  heating  and  cooling  curves 
from  which  the  thermal  critical  points  are  determined.  In 
order  to  emphasize  the  existence  of  such  critical  points  and 
then  determine  their  location  more  accurately  the  data  are 
plotted  in  a  number  of  different  ways. 


FIG.  61. 


232 


PHYSICAL  CHEMISTRY 


i.  The  time-temperature  curve.  In  this  method  the 
coordinates  are  the  time  /  in  seconds  and  the  temperature 
6.  The  ordinates  are  the  successive  rises  (or  falls)  of  tem- 
perature, and  the  abscissas  the  corresponding  time  in  seconds 
when  the  temperature  readings  are  made  counting  from  the 
beginning  of  the  observations.  The  data  for  a  cooling  curve 


850* 


Temperature-Time 
curve 


830'- 


8tOf- 


B 


/nverserate 
curve 


D/ftenence 
ct/rre 


Derweef-d/ffer- 
entia/  curve. 


LFio.  62. —  TYPES  OF  Cooling  Curves  —  Desch. 

showing  two  critical  points  are  represented  by  this  method 
by  curve  A  in  Fig.  62. 

2.  Inverse-rate  curve.  If  the  temperatures  are  plotted 
against  the  actual  interval  of  time  required  for  each  successive 
change  of  i°  C.  in  temperature,  we  have  what  is  known  as 

the  inverse-rate  curve,  such  as  C  in  Fig.  62.     —  -  represents 

the  change  in  time  required  for  a  change  in  temperature  and 
gives  us  the  time  required  for  cooling  through  i°.  Plotting 
these  values  against  the  temperatures  0,  we  have  as  the 

coordinates  0  and  — . 

The  fact  that  the  slight  retardation  in  rate  of  cooling 
might  be  overlooked,  owing  to  the  small  jogs  in  the  curves, 
suggested  to  Osmond  the  desirability  of  emphasizing  these 
thermal  points  by  using  the  inverse-rate  curves,  the  breaks 
in  which  are  approximately  proportional  to  the  amount  of 


SOLUTION  OF  SOLIDS   IN  LIQUIDS  233 

heat  evolved  on  cooling  or  absorbed  on  heating.  To  still 
further  overcome  the  irregularities  and  effects  of  the  furnace 
and  other  surrounding  influences,  use  is  made  of  neutral 
bodies,  the  cooling  of  which  is  compared  with  that  of  the 
sample  to  be  tested.  Robert  Austen  introduced  the  use  of  a 
neutral  body  and  two  thermocouples,  so  that  the  difference 
of  temperature  between  it  and  the  sample  to  be  tested 
could  be  determined,  as  well  as  the  actual  temperature  of  the 
metals.  The  temperature  of  the  two  would  be  the  same  if 
the  heat  capacities  and  emissivities  were  identical,  and 
they  would  be  different,  only  at  the  critical  points,  where 
heat  is  evolved  on  cooling  or  absorbed  on  heating.  There 
will  always  be  a  little  lagging  in  one  of  the  substances,  for 
they  will  not  have  the  same  heat  capacities,  but  the  critical 
points  will  be  represented  by  abrupt  differences  between  the 
temperatures  of  the  two  bodies. 

3.  Difference  curves.     By  employing  a  neutral  body  that 
shows  no  thermal  inversion  points,  and  plotting  the  difference 
in  temperature  between  the  neutral  body  and  the  one  under 
examination  against  the  temperatures,  we  then  have  as  the 
coordinates  the  temperature  0  and  0  —  0{.     Such  a  difference 
curve  is  represented  by  D  in  Fig.  62,  while  the  curve  desig- 
nated B  represents  the  temperature-time  cooling  curve  for  a 
neutral  body. 

4.  Derived  differential  curve.     If  the  slope  of  the  difference 
curve  is  plotted  against  the  temperature,  we  have  as  the 
coordinates  the  temperature  0,  and  the  rate  of  cooling  for 

each  degree  of  temperature  — - — - — — .     This  is  the  method 

A  6 

employed  by  Rosenhain  and  is  represented  by  curve  E  in 
Fig.  62.  This  method  gives  the  most  pronounced  indication 
of  the  thermal  critical  points,  as  is  readily  seen  from  a 
comparison  of  these  different  curves,  and  thus  eliminates 
more  completely  the  irregularities  which  are  due  primarily 
to  the  differences  of  the  heat  capacities  and  emissivities  of 


234  PHYSICAL   CHEMISTRY 

the  neutral  body  and  the  sample  under  examination  resulting 
from  their  different  rates  of  cooling  and  heating. 

Figure  63  represents  a  typical  fusion  curve  of  binary  alloys 
whose  metals  form  solid  solutions.  For,  if  at  some  concen- 
tration, such  as  50  per  cent  of  A  and  50  per  cent  of  B,  we 

have  the  liquid  at  the  tempera- 
ture t  represented  by  the  point  P, 
and  if  we  cool  the  melted  mass 


we  reach  the  liquidus  curve  AlB 
at  the  point  /  temperature  tt. 
Solidification  begins  and  the  crys- 
tals that  separate  must  have  the 

_       composition  represented  by  5  on 
100°/&  i0°^°   t]^e  so^dus  curve,   which    is  ob- 


FIG 6 

tained  by  drawing  a  horizontal  line 

through  I  until  it  intersects  the  solidus  curve  at  s.  This 
must  represent  the  composition  of  the  crystals  that  separate. 
This  is  designated  a  solid  solution. 

Now  as  the  mass  continues  to  cool  from  tt  to  tlt,  the  solid 
crystals  that  separate  at  I'  continue  to  grow  and  become 
richer  and  richer  in  the  metal  A,  while  the  remaining  mother 
liquid  likewise  becomes  richer  in  A  and  therefore  more 
fusible.  The  varying  composition  of  the  liquid  is  represented 
by  the  part  of  the  curve  //'•••  A,  and  at  any  temperature 
the  composition  of  the  crystals  is  designated  by  5  on  the 
solidus  curve,  and  at  the  still  lower  temperature  tv  by  s', 
etc.  This  means  that  the  crystals  that  separate  out  on 
cooling  change  in  composition  from  s,  through  5'  to  A 
represented  by  the  solidus  curve.  This  means  that  the  crys- 
tals first  formed  increase  in  size  by  addition  of  crystals  of 
different  composition,  but  as  the  temperature  falls  diffusion 
takes  place,  and  the  crystals  become  homogeneous.  At  the 
temperature  tw  the  solidification  is  complete,  and  the  com- 
position of  the  last  drop  of  molten  liquid  to  solidify  has  the 
composition  of  nearly  pure  A. 


SOLUTION  OF  SOLIDS   IN  LIQUIDS 


235 


Diffusion  takes  place  readily  in  the  case  of  liquid  solutions, 
but  to  produce  homogeneous  crystals  with  solid  solutions 
the  solidification  and  subsequent  cooling  must  be  very  slow, 
otherwise  the  solid  solutions  will  be  heterogeneous,  that  is, 
the  different  layers  on  the  crystals  may  be  of  different  com- 
position, the  proportion  of  the  more  fusible  metal  increasing 
from  the  inside  to  the  outside.  By  heating  the  alloy  a  long 
time  at  a  temperature  below  the  melting  point,  diffusion 
takes  place  and  destroys  the  heterogeneous  structure  of  the 
solid  solution.  This  is  designated  the  annealing  process. 

This  will  become  clearer  if  we  give  a  specific  example. 
In  Fig.  64  we  have  the  temperature-concentration  diagram 
of  the  fusibility  curves  for  gold  and  platinum,  which  are 
typical  of  such  isomorphous  pairs  of  solids.  AlB  is  the 
liquidus  curve  and  AsB  the  solidus  curve,  and  in  the  area 
between  the  two  the  alloys  are  partially  liquid  and  partially 
solid.  In  Fig.  65  for  Cu  and  Ni  series,  this  area  is  much 


I     * 


1007, 


FIG.  64. 


FIG.  65. 


smaller  than  in  the  Au-Pt  series.  If  a  Cu-Ni  alloy  is  rapidly 
cooled,  it  will  be  much  more  nearly  homogeneous  than  an 
alloy  of  Au-Pt  when  cooled  under  the  same  conditions. 
There  is  less  difference  in  the  composition  of  the  liquid  and 
the  solid  which  separates,  and  consequently  incompleteness 
of  equilibrium  has  a  less  influence  in  the  case  of  Cu-Ni  than 
in  the  case  of  Au-Pt.  It  is  conceivable  that  the  liquidus  and 
solidus  curves  may  be  so  close  together  that  it  would  be  practi- 


*•. 
236  PHYSICAL   CHEMISTRY 

cally  impossible  to  distinguish  them,  and  then  the  solid  and 
liquid  phases  in  equilibrium  would  be  identical  in  composition. 
The  type  of  freezing  curve  depends  upon  the  mutual  action 
of  the  pairs  of  liquids  selected.  In  the  cases  just  considered 
we  have  systems  the  components  of  which  form  no  chemical 
compounds,  and  the  crystals  that  separate  are  miscible  in  all 
proportions,  forming  solid  solutions.  Now  it  is  conceivable 
that  the  restriction  that  no  chemical  compound  formed  by 
the  action  of  the  constituents  can  be  removed,  and  also  that 
the  crystals  separating  may  be  nonmiscible  or  insoluble. 
It  is  then  possible  to  classify  these  various  binary  systems 
upon  the  basis  of  the  freezing-point  curves  as  follows : 

I.  The  freezing-point  curve  represents  a  complete  series  of 
mixed  crystals  or  solid  solutions  which  are  miscible  in  all 
proportions. 

i.   The  freezing  points  of  all  possible  mixtures  of  the  two 
metals  A  and  B  in  Fig.  66  are  intermediate  between  the 
freezing  point  of  A  and  that  of  B. 
B  The  curve  AlB  represents  the  freezing 
points  of  the  molten  masses  and  AsB 
the  solidus  curve  which  represents  the 
composition    of    the    solid    solutions 
which  separate  when  these  mixtures 
solidify  completely.     These  solid  solu- 


FIG.  66.  tions  vary  in  concentration  as  indi- 

cated by  the  horizontal  axis. 

2.  The  freezing-point  curve  shows  a  maximum  freezing 
point.  That  is,  by  the  addition  of  B  to  A  the  freezing  point 
is  raised  until  a  certain  concentration,  C,  is  reached,  when 
the  maximum  value  is  obtained.  Likewise  when  A  is 
added  to  liquid  B  the  freezing  point  of  the  solution  is  higher 
than  that  of  the  pure  solvent  B.  As  the  concentration  of  A 
increases,  the  freezing  point  of  the  solution  increases  until  a 
concentration  is  reached  which  gives  the  solution  of  the 
maximum  freezing  point,  designated  by  C  in  Fig.  67.  Now 


SOLUTION  OF   SOLIDS   IN  LIQUIDS 


237 


FIG.  67. 


if  a  solution  of  B  in  A  be  allowed  to  cool,  at  the  freezing 
point  t.j  the  crystals  which  separate  will  be  richer  in  B 
than  the  solution  from  which  they  separate,  as  s,  and  simi- 
larly for  other  solutions,  we  have  a 
series  of  points  representing  the  con- 
centrations of  the  solid  solutions  sep- 
arating, and  these  are  represented  by 
the  solidus  curve  AsC.  At  the  point 
C  the  composition  of  the  solid  which 
separates  is  the  same  as  that  of  the 
solutions,  that  is,  the  whole  mass 
solidifies.  Similarly  the  curve  Cl'B 
represents  the  liquidus  curve  for  solutions  rich  in  B,  and 
the  corresponding  solidus  curve  is  represented  by  Cs'B. 
The  liquidus  and  solidus  curves  coincide  at  this  point,  C, 
and  we  have  an  equilibrium  when  the  molten  mass  solidifies 
without  change  of  temperature,  as  in  the  case  of  a  pure 
substance,  and  the  structure  of  an  alloy  of  the  composition 
represented  by  C  will  be  completely  homogeneous. 

No  examples  of  this  case  are  known  among  alloys,  but  the 
system  d-  and  /-carvoxim  shows  this  type  of  freezing-point 
curve. 

3.  The  freezing-point  curve  shows  a  minimum  freezing 
point.  The  curve  AlC,  Fig.  68,  rep- 
resents the  liquidus  curve  of  alloys  rich 
in  A,  and  AsC  its  corresponding  solidus 
curve,  which  shows  that  the  composi- 
tion of  the  solid  solutions  that  separate 
is  richer  in  A  than  that  of  the  solutions 
from  which  they  separate.  Likewise 
the  curve  Cl'B  represents  the  liquidus 
curve  of  the  alloys  rich  in  B  ;  and  Cs'B 
its  corresponding  solidus  curve,  which  shows  that  the  compo- 
sition of  the  solid  solutions  which  separate  is  richer  in  B 
than  that  of  the  solutions  from  which  they  separated.  At 


FIG.  68. 


PHYSICAL  CHEMISTRY 


the  point  C  the  crystals  and  the  liquid  from  which  they 
separate  have  the  same  composition,  and  the  alloy  is  crys- 
tallized at  constant  temperature  and  must  be  homogeneous. 
Binary  systems  of  alloys  which  belong  to  this  type  of 
curves  are  Mn-Cu  and  Mn-Ni. 

It  is  conceivable  that  one  or  more  minimum  or  maximum 
points  may  occur  in  the  same  system,  and  that  even  a  com- 
bination of  these  three  types  might  be  present,  thus  giving 
rise  to  a  very  complicated  cooling  curve.  Such  combina- 
tions are  represented  in  Fig.  69.  In  I  the  addition  of  B 
to  A  raises  the  melting  point,  and 
the  addition  of  A  to  B  lowers  the 
melting  point,  while  at  C  there  is  a 
considerable  range  of  concentration 
over  which  the  liquidus  and  solidus 
curves  are  the  same,  and  we  have 
a  marked  horizontal  inflection  of  the 
curve.  It  is  possible  to  overlook  such 


FIG  09  °  10°* a  condition  in  plotting  the  experi- 
mental determinations  of  the  cooling 
curve,  but  the  halting  of  the  crystallization  interval  would  be 
much  more  pronounced  than  at  other  portions  of  the  curve 
where  no  such  intervals  of  crystallization  take  place.  The 
systems  Br-I  and  Mg-Cd  are  examples  of  this  type  of  fusion 
curves.  There  are  no  known  examples  of  the  curves  II  and 
III  shown  in  Fig.  69. 

By  a  consideration  similar  to  that  employed  in  connection 
with  fractional  distillation  it  can  be  readily  shown  that  Type 
I,  i  represents  the  only  pairs  of  binary  mixtures  that  can  be 
completely  separated  by  fractional  crystallization. 

II.  Freezing-point  curves  which  do  not  represent  a  continuous 
series  of  mixed  crystals  or  solid  solutions  and  which  are  not 
miscible  in  all  proportions. 

i.  The  freezing-point  curves  of  a  binary  system  which 
meet  at  a  transition  point  form  two  series  of  solid  solutions. 


SOLUTION  OF   SOLIDS   IN  LIQUIDS 


239 


"* 


F 


This  type  of  freezing-point  curves  is  represented  by  the 
system  Hg-Cd,  Fig.  70.  The  two  liquidus  curves  for  this 
system  are  A  B  and  BC. 

The  solid  solution  richer  in  Hg  separates  along  the  solidus 
curve  AD,  and  the  solid  solution  richer  in  Cd  separates 
along  the  solidus  curve  EC,  and 
at  the  point  of  intersection,  B, 
of  the  two  liquidus  curves  we 
have  the  two  solid  solutions  in 
equilibrium.  At  this  tempera- 
ture, 1 88°  C.,  the  two  solid  solu- 
tions separating  have  the  com- 
position represented  by  D  (62.7 
atomic  per  cent  of  Cd)  and  E 
(65.2  atomic  per  cent  Cd)  and 
are  in  equilibrium  with  the  liquid  of  the  composition 
represented  by  B  (51  atomic  per  cent  Cd).  B  is  a  transition 
point,  where  we  have  the  transition  of  one  series  of  crystals 
into  the  other  taking  place  at  constant  temperature,  as 
represented  by  the  horizontal  line  BDE.  Along  the  liquidus 
curve  BC  we  have  crystals  of  one  solid  solution  (b)  separating, 
and  along  AB  crystals  of  another  solid  solution  (a).  So  we 
may  divide  our  diagram  into  the  following  areas : 

Above  the  freezing-point  curve  ABC  the  alloys  of  Hg-Cd 
are  liquid.  All  alloys  of  which  A  B  is  the  liquidus  solidify 
with  the  separation  of  crystals  of  the  solid  solution  a,  and  the 
area  inclosed  between  the  liquidus  curve  AB  and  the  solidus 
curve  AD  contains  crystals  of  this  solid  solution  and  the  liquid, 
and  at  temperatures  below  that  represented  by  the  solidus 
curve  we  have  only  solid  solution  a. 

All  alloys  with  a  Cd  concentration  greater  than  represented 
by  E  consist  of  crystals  of  the  solid  solution  b,  and  those 
between  concentrations  designated  by  D  and  E  consist  of  a 
mixture  of  crystals  of  two  solid  solutions,  a  and  b,  and  the 
solid  alloy  is  a  mixture  of  a  and  b,  as  represented  by  the  area 


240  PHYSICAL  CHEMISTRY 

marked  FDEG.  That  is,  we  have  a  solution  of  the  one  in 
the  other,  and  as  the  solubility  is  dependent  upon  the  tem- 
perature, the  curves  DF  and  EG  represent  their  mutual 
solubility,  decreasing  with  decrease  of  temperature.  This  is 
the  area  where  we  have  the  crystals  a  and  b  existing  together. 
It  is  analogous  to  the  system  aniline  and  water,  Fig.  16, 
wherein  the  area  inclosed  within  the  equilibrium  curve 
represents  the  area  of  mixtures  which  separate  into  two  liquid 
layers,  the  compositions  of  which  are  represented  by  some 
points  on  the  two  limbs  of  the  equilibrium  curve.  If  a 
mixture  of  a  composition  intermediate  between  that  rep- 
resented by  the  lines  fF  and  gG  be  cooled  sufficiently  low, 
say  to  about  —  40°,  they  will  eventually  separate  into  the  two 
types  of  solid  crystals  a  and  6,  but  if  the  composition  is 
richer  in  Hg  than  indicated  by  fF,  only  a  crystals  will  appear, 
and  if  richer  in  Cd  than  indicated  by  gG,  the  crystals 
will  be  b. 

If,  however,  a  solution  of  the  composition  as  represented 
by  m  be  solidified,  it  will  consist  wholly  of  the  solid  solution 
whose  crystals  are  a  only ;  but  if  this  be  cooled,  the  curve  FD 
will  be  intersected  and  the  solid  solution  will  separate  into 
two  nonmiscible  isomorphous  mixtures  which  are  represented 
by  n  and  o  respectively.  The  curves  DnF  and  EoG  represent 
the  change  in  concentration  of  the  two  sets  of  mixed  crystals 
which  are  in  equilibrium  at  different  temperatures.  That 
is,  we  have  a  change  in  the  composition  of  the  mixed 
crystals  with  a  change  in  temperature,  which  is  again  our 
annealing  process,  and  in  the  production  of  alloys  this  is  of 
very  great  importance,  as  the  physical  properties  depend 
upon  the  type  of  mixed  crystals  present. 

The  freezing-point  curves  of  liquid  solutions  of  MgSiO3  and 
MnSiO3  are  represented  in  Fig.  71.  We  have  in  this  case 
the  melting  point  of  all  mixtures  of  MgSiO3  and  MnSiO3 
intermediate  between  that  of  the  two  components.  Along 
one  part  of  the  freezing-point  curve  A  B  one  set  of  solid 


SOLUTION  OF  SOLIDS   IN  LIQUIDS 


241 


solutions  separate,  and  along  CB  another  set  of  solid  solu- 
tions separate,  and  at  their  point  of  intersection,  B,  we  have  a 
marked  discontinuity  represented.  For  this  pair  of  binary 
mixtures  this  is  at  1328°  and  is  known  as  the  transition  point. 
The  composition  of  the  two  solid 
solutions  that  separate  at  the 
transition  point  B  is  designated  by 
D  and  E. 

The     freezing-point     curves 


2. 


FIG.  71. 


show  a  eutectic  point  and  the  crys- 
tals separated  are  partially  miscible 
(Roozeboom's  Type  5). 

The  binary  system  Cu-Ag  is  an 
illustration,  Fig.  72,  of  this  type  of  fusion  curve,  which 
has  been  worked  out  very  carefully.  Along  the  liquidus 
curve  CB  the  crystals  of  the  solid  solution  a,  which  is  a 
solution  of  Cu  in  Ag,  separate.  The  composition  of  this 
solid  solution  varies,  as  indicated  by  the  curve  CE.  Like- 
wise along  the  liquidus  curve  AB  the  solid  solution  b 
separates,  and  at  the  intersection  B  of  the  two  liquidus 
curves  the  concentration  of  the  two  solutions  which  sepa- 
rate is  designated  by  D  and  E.  These  represent  saturated 
solutions  which  are  in  equilibrium  at 
the  point  B.  This  is  designated  a 
eutectic  point  and  indicates  a  marked 
arrest  during  which  the  temperature 
remains  constant  while  the  mass 
solidifies.  The  eutectic  is  then  com- 
posed of  a  saturated  solid  solution  of 
Cu  in  Ag,  represented  by  E,  and  of 
a  saturated  solid  solution  of  Ag  in 
Cu,  represented  by  D.  Just  as  any  two  partially  miscible 
liquids  have  different  solubilities  at  different  temperatures, 
so  these  partially  miscible  solid  solutions  have  a  solubility 
curve  analogous  to  that  of  liquids  such  as  aniline  and  water. 


FIG.  72. 


242 


PHYSICAL  CHEMISTRY 


USiO, 


FIG.  73. 


100* 
MfiSiO, 


We  may  then  consider  the  curves  DF  and  EG  portions  of 
the  solubility  curves  of  these  partially  miscible  solid  solutions. 
Figure  73  represents  the  freezing-point  curves  for  Li2SiO3 
and  MgSiO3.  AC  and' CB  are  the  freezing-point  curves, 
and  C  is  the  eutectic  point.  If  any  liquid  solution  of  these 
two  substances  be  selected  at  a  tem- 
perature and  concentration  repre- 
sented by  P,  and  if  this  be  cooled 
to  the  temperature  at  which  we 
meet  the  freezing  curve  CB  at  D, 
the  solution  will  freeze,  and  the 
solid  phase  will  separate ;  as  the 
solid  in  this  particular  case  is  a 
mixture  of  Li2SiOs  and  MgSiO3,  its 
concentration  may  be  represented  by  some  such  point 
as  E,  richer  in  Mg  than  the  solution  from  which  it 
was  separated,  and  the  liquid  will  become  richer  in  the 
other  component.  We  can  obtain  the  composition  of  the 
other  solids  separating,  which  we  represent  by  the  curve 
BEG,  while  similarly  AF  represents  the  solids  separating 
along  the  curve  AC.  AC  and  CB,  representing  the  freezing 
points  of  liquid  solutions,  are  designated  the  liquidus  curves, 
and  AF  and  BG,  representing  the  melting  points  of  the  solid 
solutions,  are  termed  the  solidus  curves. 
At  the  eutectic  point  C  the  solid  phase 
separating  is  a  eutectic  consisting  of  two 
solid  solutions  of  the  concentrations 
represented  by  F  and  G.  The  area 
between  the  liquidus  and  solidus  curves 
represents  both  liquid  and  solid. 

In  the  case  of  Zn-Al  alloys,  Fig. 
74,  it  will  be  noted  that  the  satu- 
rated solutions  of  Zn  contain  but  a  small  quantity  of 
Al,  whereas  solutions  of  Al  contain  a  very  much  larger 
quantity  of  Zn.  The  eutectic  C  is  composed  of  these  two 


SOLUTION  OF   SOLIDS   IN  LIQUIDS  243 

solid  solutions,  D  and  E,  and  the  concentration  D  of  the  solid 
solution  of  Al-Zn  is  nearly  over  to  the  pure  zinc  concentration. 

III.  The  components  of  the  binary  system  form  chemical 
compounds  and  the  freezing-point  curves  show  one  or  more 
chemical  compounds. 

It  is  conceivable  that  a  conglomerate  consisting  of  mixed 
crystals  may  not  only  melt  at  constant  temperature,  as  in  the 
case  of  eutectic  mixtures,  but  also  that  they  may  be  in  such 
a  proportion  as  to  conform  to  the  laws  of  definite  and  multiple 
proportions,  when  we  should  have  a  pure  chemical  compound 
separating,  which  would  also  be  characterized  by  the  liquid 
solution  solidifying  completely  without  change  of  temperature. 
In  Fig.  75  we  have  represented  the 
freezing-point  curves  for  solutions  of 
K2SO4  and  MgSO4  above  700°  C. 
Along  AB  the  solid  phases  separating 
are  solid  solutions,  and  along  ED  pure 
MgSO4.  At  B  and  D  we  have  two 
eutectic  points  at  747°  and  884°  re- 
spectively. The  curve  BCD  represents 
the  solubility  or  freezing-point  curve  of  the  chemical  com- 
pound of  composition  C,  which  is  K2SO4  •  2  MgSO4  and 
known  as  the  mineral  Langbeinite,  with  a  melting  point  of 
927°.  Along  the  curve  CB  the  solid  phase  which  crystal- 
lizes is  this  mineral,  and  the  liquid  becomes  richer  in  K2SO4 
until  the  concentration  B  is  reached,  when  the  whole  mass 
solidifies  into  the  conglomerate,  the  solid  solution  F  and 
K2SO4  •  2  MgSO4,  without  change  of  temperature.  Along  CD, 
the  solid  phase  which  separates  is  K2SO  •  2  MgSO4 ;  the  liquid 
solution  becomes  richer  in  MgSO4  until  the  concentration  of 
the  eutectic  is  reached,  when  it  will  solidify  without  change 
of  temperature  at  884°,  and  the  mixed  crystals  will  be  a  con- 
glomerate of  the  mineral  K2SO4  •  2  MgSO4  and  pure  MgSO4. 

The  complete  concentration-temperature  diagram  for 
Mg-Sn  is  given  in  Fig.  76,  in  which  the  curve  ABCDE 


244 


PHYSICAL   CHEMISTRY 


represents  the  fusion  curve.  It  is  composed  of  three 
branches,  AB,  BCD,  and  DE,  along  each  of  which  there  is 
a  separate  definite  crystalline  variety  in  equilibrium  with  the 


liquid.  Along  curve  A  B  the  pure  a  (Mg)  is  in  equilibrium  ; 
along  DE,  the  pure  /3  (Sn) ;  while  along  the  fusion  curve 
BCD,  which  shows  no  discontinuity  at  C  and  is  to  be  con- 
sidered a  single  continuous  fusion  curve,  the  chemical  com- 
pound SnMg2  separates  out  along  the  whole  range  of  temper- 
atures. That  is,  in  melts  richer  than  about  70  per  cent  Sn 
and  those  richer  in  Mg  than  about  30  per  cent  Mg  to  about 
60  per  cent,  we  have  for  temperatures  above  the  eutectic 
temperature  B,  about  565°,  this  chemical  compound  existing 
in  equilibrium  with  melts  of  two  different  concentrations  at 


SOLUTION  OF  SOLIDS   IN  LIQUIDS 


245 


the  same  temperature.  The  point  C  is  a  maximum  tem- 
perature and  corresponds  to  the  melting  point  of  the  pure 
chemical  compound  SnMg2.  At  points  B  and  D  we  have 
two  marked  breaks  in  the  fusion  curve  and  these  represent 
the  two  eutectic  points  known  for  this  alloy.  The  two 
eutectic  horizontals,  aBc  and  c'De,  are  at  different  tem- 
peratures, and  their  components,  which  are  represented  by 
the  ends  of  the  lines,  are  nonmiscible.  The  eutectic  B 
separates  into  pure  magnesium  and  the  pure  chemical  com- 
pound SnMg2,  and  the  eutectic  D  separates  into  pure  SnMg2 
and  pure  Sn. 

The  method  of  obtaining  a  cooling  curve  is  represented  by 
Fig.  77,  in  which  we  have  represented  on  a  temperature- 
concentration  diagram  the  temperature-time  cooling  curves 


FIG.  77- 


246  PHYSICAL  CHEMISTRY 

for  a  number  of  alloys  of  different  concentrations,  represented 
by  the  numbers  on  the  fusion  curve  in  Fig.  76.  We  have 
the  pure  metal  Mg,  the  cooling  curve  of  which  is  represented 
by  mA  ;  the  molten  metal  cools  regularly  until  the  tem- 
perature represented  by  A  is  reached,  when  its  temperature 
is  arrested  for  the  time  Fs,  during  which  the  metal  solidifies 
completely,  and  then  the  cooling  proceeds  regularly  as  rep- 
resented by  sn.  A  melt  containing  approximately  90  per 
cent  is  cooled,  and  we  have  the  curve  mF ;  when  the  point  F 
is  reached,  the  melt  begins  to  solidify  with  the  separation  of 
pure  Mg,  and  the  solidification  continues  until  the  tempera- 
ture of  the  eutectic  B  is  reached,  when  we  have  another  arrest 
in  the  rate  of  cooling,  as  designated  by  s,  at  which  the  tem- 
perature remains  constant  until  the  remaining  liquid  has 
completely  solidified.  In  a  similar  manner  the  temperature- 
time  curves  illustrating  the  rates  of  cooling  are  deter- 
mined for  alloys  representing  the  whole  range  of  concentra- 
tion, and  the  points  F,  representing  the  initial  freezing,  are 
all  connected,  giving  us  the  heavy  line  representing  the  freez- 
ing-point or  fusion  curve  ABODE  for  the  alloys  composed  of 
Mg-Sn.  The  horizontal  portions  designated  by  5  represent 
the  eutectic  temperature,  or  the  lowest  temperature  at  which 
these  constituents  can  exist  in  the  liquid  state. 

It  will  be  noticed  that  the  time  required  for  the  solidifica- 
tion of  these  different  alloys  is  not  the  same,  and  this  is  shown 
by  the  different  lengths  of  the  horizontal  sections  represented 
by  s.  This  indicates  that  there  is  more  of  the  eutectic 
present,  and  consequently  more  time  is  required  for  its  solidi- 
fication, and  the  temperature  therefore  remains  constant  for 
a  greater  length  of  time.  We  therefore  have  an  indication 
of  the  relative  quantities  of  the  constituents  present  with 
the  eutectic  alloy. 

Methods  have  been  employed  to  represent  graphically 
the  per  cent  of  the  eutectic  present  in  any  particular  solidified 
melt.  This  is  shown  by  the  dotted  portion  of  the  diagram  in 


SOLUTION  OF  SOLIDS   IN  LIQUIDS  247 

Fig.  76.  Draw  the  line  Bb  of  a  length  representing  100  per 
cent,  and  since  at  B  the  melt  all  solidifies  to  eutectic,  then 
this  is  the  maximum  quantity  of  the  eutectic  that  can  be 
produced  from  the  melt,  since  all  of  the  melt  goes  over  into 
the  eutectic  without  change  of  temperature.  At  a,  which 
represents  pure  Mg,  there  would  be  no  eutectic,  hence  the 
quantity  would  be  zero  per  cent ;  the  same  is  true  for  c, 
which  represents  all  pure  SnMg2  and  no  eutectic.  Con- 
necting these  points  with  b  we  have  the  percentage  of  the 
eutectic  in  the  solidified  melt  of  any  specified  concentration, 
such  as  i,  2,  3,  5,  6,  etc.,  represented  by  the  distances  from 
the  base  line  aBc.  If  the  distance  from  this  line  to  b  were 
divided  into  100  parts,  the  percentage  of  the  eutectic  alloy 
in  the  solidified  melt  could  be  readily  ascertained.  The 
same  is  true  for  the  eutectic  D  and  the  per  cent  it  is  of  any 
melts  above  approximately  70  per  cent  Sn,  the  structural 
composition  of  the  solidified  melt  being  represented  by  the 
curve  c'de  drawn  upon  the  base  c'De.  Many  times,  these 
are  drawn  with  the  base  line  the  same  as  that  of  the  con- 
centration axis,  and  a  convenient  distance  on  the  vertical 
axis  taken  as  100  per  cent  for  the  eutectic  D.  These  different 
solidified  melts  have  their  characteristic  microscopic  appear- 
ance, and  the  different  mixed  crystals  are  readily  distin- 
guished and  the  different  components  thus  recognized. 


CHAPTER  XXII 


APPLICATIONS   OF  THE  PHASE  RULE 

THE  number  and  nature  of  the  phases  possible  to  any  sys- 
tem when  in  equilibrium  depend  on  the  composition  and  the 
temperature,  and  it  is  due  largely  to  the  application  of  the 
Phase  Rule  to  the  study  of  alloys  that  such  marked  progress 
has  been  made  in  the  last  few  years.  So  we  shall  confine  our 
consideration  of  the  application  of  this  rule  to  the  study  of 
alloys  primarily. 

COPPER-ZINC  ALLOYS 

In  Fig.  78  we  have  reproduced  Shepard's  freezing-point 
curve  for  alloys  of  copper  and  zinc.  This  cooling  liquidus 

curve  consists  of  six  branches, 
thus  showing  the  existence  of  six 
different  solid  solutions;  but 
there  are  no  chemical  compounds 
of  copper  and  zinc  such  as  we 
found  in  the  case  of  magnesium 
and  tin.  There  is  a  distinct  solid 
solution  in  equilibrium  with  each 
of  the  six  branches  of  the  freezing- 
point  curve. 

Along  the  section  of  the  liquidus  curve  designated  AB 
homogeneous  a  crystals  separate,  the  composition  of  which 
is  represented  by  the  solidus  curve  A  b,  thus  showing  that 
the  left-hand  portion  of  the  diagram  from  the  Cu  axis  over 
to  the  line  bbi,  which  represents  about  65  per  cent  of  copper, 
consists  of  a  crystals.  The  area  between  the  solidus  curve 

248 


FIG.  78. 


APPLICATIONS  OF  THE   PHASE  RULE  249 

A  b  and  the  liquidus  curve  AB  represents  a  crystals  with  the 
mother  liquor.  The  area  BbbiBi  is  occupied  by  a  and  ft 
crystals,  the  latter  being  stable  along  the  freezing  curve  BC, 
and  the  area  cBB\c\  gives  the  limits  of  the  solid  solution,  the 
composition  of  which  varies  greatly  with  the  change  in  tem- 
perature. At  the  lower  temperature  the  ft  crystals  break 
down  along  the  line  BBi  with  the  formation  of  the  homo- 
geneous a  crystals,  while  along  the  line  cc\  they  break  down 
with  the  formation  of  7  crystals.  The  existence  of  a  and  7 
crystals  in  the  same  ingot  has  not  been  discovered ;  ft  and  7 
exist  in  the  area  Ccc\C\,  while  7  is  in  equilibrium  along  the 
portion  of  the  liquidus  curve  designated  CD,  and  the  area 
CCidid  is  the  field  of  pure  7  crystals,  d  crystals  form  from 
the  melt  along  DE,  while  at  lower  temperatures  these  break 
down,  forming  5  and  €  crystals  or  e  and  7  crystals.  The 
transformation  of  e-5  into  e  crystals  is  so  marked  that  it  can 
be  accurately  observed  to  29  per  cent  of  copper.  The  exact 
position  of  des  is  not  definitely  known,  but  it  lies  between  20 
and  3 1  per  cent  of  copper.  Below  d^e^e^  the  alloy  consists  of 
the  mixed  crystals  of  7  and  e.  The  e  crystals  separate  out 
along  the  liquidus  EF,  and  these  solid  solutions  vary  in  con- 
centration from  13  to  20  per  cent  of  copper.  Alloys  of  copper 
and  zinc  containing  from  2.5  to  14  per  cent  of  copper  when 
solid  consist  of  the  mixed  crystals  c  and  77,  the  77  crystals 
being  stable  along  that  part  of  the  cooling  curve  designated 
FG.  Below  concentrations  less  than  2.5  per  cent  of  copper, 
the  solid  alloy  consists  of  homogeneous  solid  solutions  of  77. 

Muntz's  metal,  which  contains  60  per  cent  copper,  is 
composed  at  ordinary  temperatures  of  the  a  and  ft  crystals, 
but  if  quenched  above  750°  it  will  consist  of  homogeneous  ft 
crystals,  which  make  the  brass  ductile  at  temperatures  above 
750°  so  that  it  may  be  rolled  hot.  ft  crystals  are  less  ductile 
at  lower  temperatures  than  the  a  crystals.  Quenched  from 
temperatures  above  750°,  Muntz's  metal  is  harder  and 
stronger  but  less  ductile  than  the  annealed  alloy. 


250 


PHYSICAL   CHEMISTRY 


These  different  mixed  crystals  are  readily  recognized  under 
the  microscope,  and  by  means  of  micro-photographs  the  heat 
treatment  of  brass  has  been  carefully  studied. 

IRON-CARBON  ALLOYS 

Among  the  binary  alloys,  that  of  iron  and  carbon  is  perhaps 
the  most  important.     The  complexity  of  the  system  is  much 
increased  by  the  fact  that  iron  exists  in  three  allotropic  modi- 
Steel  Cast  Iron 


lOO8/. 


.Per  cent  Carbon 
Metastajble  or  Cementite-Austentite  Carbon-Iron  Diagram  (Howe) 


FIG.  79. 

fications :  a,  /3,  and  y  forms.  Howe's  carbon-iron  equilib- 
rium diagram  is  given  in  Fig.  79.  The  melting  point  of 
pure  iron  is  1530°.  The  three  allotropic  modifications  of 


APPLICATIONS   OF  THE   PHASE   RULE  251 

iron  all  crystallize  in  the  regular  system,  and  as  there  are 
decided  energy  and  volume  changes  at  their  points  of  trans- 
formation, there  are  evidences  of  discontinuity  in  the  cooling 
curve  of  pure  iron,  and  consequently  proof  of  the  different 
physical  modifications.  The  7-iron  is  the  stable  form  above 
920°,  where  it  passes  on  cooling  into  0-iron  with  the  evolu- 
tion of  heat  and  a  considerable  expansion  of  volume.  7-iron 
has  a  marked  solvent  power  for  carbon,  and  AB,  the  liquidus 
curve,  represents  the  freezing  points  of  solutions  of  carbon 
in  iron,  while  AE,  the  solidus  curve  (melting  point  curve), 
"  represents  the  temperature  at  which  the  alloys  have  just 
completed  their  freezing  process,  that  is,  have  just  become 
completely  solid  ;  or  conversely  it  represents  the  temperature 
of  incipient  fusion  on  heating  "  (Rosenhain).  "  The  method 
of  determining  the  solidus  was  to  take  small  pieces  of  steel 
of  known  composition,  heat  these,  and  suddenly  cool  them 
from  successively  higher  temperatures;  afterwards,  each 
specimen  was  examined  by  means  of  the  microscope.  It  is 
easy,  as  the  photographs  show,  to  determine  what  is  the 
particular  point  at  which  you  have  reached  a  temperature 
where  there  was  a  small  quantity  of  liquid  metal  present 
at  the  moment  of  quenching." 

Critical  Thermal  Points  of  Pure  Iron.  —  When  pure  iron 
is  cooled  from  a  high  temperature  (1000°  or  above),  the  cool- 
ing proceeds  slowly  and  regularly,  then  it  is  arrested  for  a 
considerable  time  while  the  temperature  remains  constant, 
and  in  some  instances  the  temperature  of  the  cooling  sample 
of  iron  actually  rises  ;  the  metal  becomes  hotter,  it  recalesces  ; 
hence  the  name  recalescence  is  given  to  this  particular  critical 
thermal  point.  This  recalescence  or  glow  of  the  steel  may 
be  readily  seen  if  the  experiment  is  conducted  in  a  darkened 
room.  Eschernoff  designated  such  critical  points  by  A, 
and  to  distinguish  those  obtained  on  cooling  from  those  on 
heating,  it  has  been  agreed  to  designate  the  former  by  Ar 
(from  the  French  refroidissement,  meaning  cooling)  and  the 


252  PHYSICAL   CHEMISTRY 

latter  by  Ac  (from  the  French  chauffage,  heating).  These 
critical  points  Ar  and  Ac  do  not  occur  at  exactly  the  same 
temperature,  and  for  steel  are  as  much  as  25°  to  50°  apart. 
This  lagging  of  the  critical  point  on  cooling  behind  the  criti- 
cal point  on  heating  is  the  physical  phenomenon  known  as 
hysteresis  and  is  due  to  the  delayed  transformation.  The 
equilibrium  temperature  at  which  the  transformations  actu- 
ally occur,  designated  by  Ar  and  Ac,  is  distinguished  from 
the  equilibrium  temperature  Ae,  at  which  they  are  due  to 
occur. 

If  a  molten  steel  of  low  carbon  content  (less  than  about 
0.4  per  cent  carbon),  represented  by  the  linej,  be  cooled,  it 
will  begin  to  freeze  with  the  formation  of  crystals  of  the  solid 
solution  termed  austenite,  the  composition  of  which  is  poorer 
in  carbon  than  the  solution  from  which  they  separated,  and 
these  crystals  are  represented  in  composition  by  the  solidus 
curve  Aj"E,  while  Aj'B  is  the  liquidus  curve.  On  further 
cooling  there  is  no  change  in  the  austenite  until  about  805° 
is  reached,  when  the  transformation  into  /3-iron  occurs,  which 
consists  in  the  separation  of  pure  /3-iron.  The  concentration 
of  the  austenite  remaining  is  represented  by  the  curve  Ar$ 
(GO)  until  the  temperature  780°  is  reached  at  jiv,  when  a- 
ferrite  appears,  and  as  the  temperature  is  further  lowered 
more  of  this  is  separated  from  the  austenite,  the  composition 
of  which  is  represented  by  the  curve  Ar3.2  (OS).  On  reach- 
ing the  temperature  725°  at  the  point  jv,  the  composition  of 
the  residual  austenite  is  represented  by  5,  which  is  pearlite 
of  a  carbon  content  of  0.9  per  cent.  This  point  is  analogous 
to  a  eu  tec  tic  point,  but  we  do  not  have  the  lowest  point  at 
which  the  particular  mixture  is  a  liquid,  but  it  is  the  lowest 
transformation  point  for  austenite,  which  is  a  solid  solution. 
We  have  a  eutectoid  substance  which  consists  of  a  mixture 
of  a-ferrite  and  pearlite.  So  below  a  temperature  of  725° 
and  up  to  a  carbon  content  of  0.9  per  cent  the  solid  steel 
when  slowly  cooled  consists  of  pure  a-ferrite  and  pearlite. 


APPLICATIONS   OF  THE  PHASE   RULE  253 

On  cooling  a  mixture  containing  4.3  per  cent  of  carbon, 
represented  by  the  line  w,  the  molten  mass  of  cast  iron  re- 
mains liquid  until  the  temperature  1135°  is  reached  at  the 
eutectic  point  E  with  the  formation  of  the  eutectic  Lede- 
burite.  This  eutectic  is  a  conglomerate  consisting  of  a  mix- 
ture of  a  honeycomb  structure  of  eutectic  cementite  filled 
in  with  the  darker  masses  of  eutectic  austenite.  Cementite 
is  the  carbide  of  iron,  Fe3C,  while  the  austenite  is  iron  satu- 
rated with  carbon.  On  further  cooling  the  chemical  com- 
pound cementite  does  not  change,  but  the  austenite  changes 
over  into  pearlite  and  cementite  at  725°,  as  represented  by 


In  an  analogous  manner  the  various  concentrations  such 
as  are  represented  by  h,  k,  m,  and  p  could  be  discussed,  but 
this  would  lead  us  too  far  and  the  student  can  work  the 
changes  out  as  an  exercise. 

APPLICATIONS  TO   ANALYTICAL  CHEMISTRY 

In  the  analysis  of  multiple  component  systems  the  proper- 
ties of  the  individual  constituents  are  often  so  nearly  alike 
that  the  usual  methods  of  analysis  fail.  So  that  in  order  to 
determine  the  quantities  of  the  constituents  it  is  necessary 
to  do  this  by  some  method  wherein  the  separation  of  the 
components  of  the  system  is  not  necessary.  This  method 
of  procedure  is  dependent  on  the  relationship  established 
under  conditions  of  equilibrium  and  by  means  of  equilibrium 
diagrams  obtained  experimentally. 

In  the  case  of  the  determination  of  alcohol  in  alcoholic 
beverages  we  have  one  of  the  principal  applications  of  this 
method.  It  is  known  that  if  to  a  solution  of  alcohol  in  water 
certain  salts,  such  as  K2CO3,  NaF,  etc.,  be  added,  the  single 
liquid  solution  breaks  into  two  liquid  phases.  The  equi- 
librium is  established  between  the  two  saturated  solutions, 
and  this  equilibrium  can  be  obtained  at  the  point  at  which 


254  PHYSICAL   CHEMISTRY 

the  components  are  in  equilibrium  just  before  the  separation 
into  two  liquid  layers  occurs. 

This  equilibrium  is  dependent  on  the  reduction  of  the 
degrees  of  freedom  of  the  system  by  the  introduction  of  the 
second  liquid  layer  in  this  case,  or  the  solid  phase  in  others. 
For  at  a  given  temperature  a  definite  solution  of  alcohol 
and  water  will  dissolve  a  definite  quantity  of  the  salt  (K2CO3) , 
and  if  we  know  the  amount  of  salt,  we  then  know  the  amount 
of  alcohol  in  the  alcohol- water  mixture .  This  will  become  more 
apparent  after  the  following  consideration  of  the  special  cases. 

By  a  method  similar  to  that  described  for  obtaining  the 
equilibrium  curve  for  the  system  water-alcohol-ether,  page 
163,  the  equilibrium  curve  for  the  system  water-alcohol-salt 
may  be  constructed  on  a  triangular  diagram.  These  data 
may  be  expressed  on  a  rectangular  diagram  by  calculating 
the  amounts  of  the  alcohol  and  of  salt  (K2CO3)  in  a  constant 
quantity  of  water  and  plotting  the  results.  It  is  evident 
then  that  if  the  amount  of  salt  is  known,  the  percentage  com- 
position of  alcohol  and  of  water  can  be  calculated. 

The  actual  determination  is  made  in  the  following  manner : 
If  we  employ  the  system  water-acetone-K2CO3,  the  actual 
experimental  data  are  obtained  by  the  general  method  just 
described.  Weigh  out  100  grams  of  the  solution  of  acetone 
and  water  to  be  analyzed.  Add  K2CO3  as  a  solid,  or  in  the 
form  of  a  solution  of  known  strength,  until  the  solution 
breaks  into  two  liquid  layers.  Determine  the  amount  of 
K2CO3  added.  Render  the  solution  homogeneous  by  the 
addition  of  water,  then  titrate  back  and  forth  with  acetone 
and  water  until  the  correct  end  point  is  ascertained.  Weigh 
again  and  determine  the  amounts  of  the  solvents  added. 
Now  from  these  weights  and  the  amount  of  the  carbonate 
added  compute  the  grams  of  K2CO3  in  100  grams  of  the  sol- 
vent (water).  Referring  to  the  acetone-K2CO3  curve  the 
amount  of  acetone  can  be  obtained  and  from  this  the  per- 
centage composition  of  the  mixture. 


CHAPTER  XXIII 
OSMOTIC  PRESSURE 

BY  placing  in  pure  water  a  bladder  filled  with  alcohol 
Nollet  (1748)  observed  that  the  bladder  became  greatly 
distended,  but  it  was  not  until  many  years  later  that  this 
phenomenon  was  rediscovered  and  explanations  offered. 
Dutrochet  (1822-)  observed  that  there  were  two  currents 
connected  with  the  passage  of  liquids  through  membranes 
during  such  phenomena  as  that  just  described :  (i)  the 
principal  current  inward  through  the  membrane,  which  he 
termed  the  endosmotic  current,  and  (2)  the  secondary  one 
outward,  the  exosmotic  current ;  while  the  phenomena  were 
called  respectively  endosmosis  and  exosmosis.  Later  the 
term  osmosis  was  applied  to  the  phenomenon  as  a  whole  and 
is  the  one  now  employed. 

Graham  (1854)  employed  septa  of  different  kinds  and 
demonstrated  that,  depending  upon  the  character  of  the 
membranes  employed  and  of  the  solute  present,  both  the 
solvent  and  the  solute  would  pass  through  the  membrane ; 
while  in  the  case  of  certain  solutes  they  would  not  pass 
through.  He  utilized  this  method,  which  he  termed  dialysis, 
for  the  separation  of  substances  into  two  general  classes  — 
those  which  passed  through  the  membrane,  crystalloids,  and 
those  which  did  not  pass  through,  colloids.  Therefore  it  is 
necessary  to  distinguish  between  dialysis,  wherein  the  solute 
passes  through  the  membrane,  and  osmosis,  where  only  the 
solvent  passes  through  the  membrane.  In  this  latter  case 
the  membrane  is  said  to  be  semipermeable,  being  pervious 
to  only  one  of  the  constituents  of  the  solution,  that  is,  to  the 
solvent. 

255 


256  PHYSICAL  CHEMISTRY 

It  was  recognized  in  the  process  of  osmosis  that  some  of 
the  solute  also  appeared  on  the  side  of  the  septum  opposite 
where  the  solution  was  placed,  and  many  explanations  have 
been  offered  to  account  not  only  for  this  small  trace  of  the 
solute  passing  through,  but  also  for  the  membrane  being  per- 
vious to  the  solvent  particularly.  The  conception  of  the 
sieve  construction  of  the  membrane  supposes  it  to  be  com- 
posed of  numerous  small  openings  of  such  size  that  only  sub- 
stances with  molecules  of  small  dimensions  can  pass  through, 
while  those  substances  with  large  molecules  are  prevented 
from  going  through.  The  passage  of  small  quantities  of  some 
solutes,  such  as  sugar,  through  animal  or  vegetable  mem- 
branes was  explained  by  assuming  the  openings  to  be  of  such 
size  that  in  the  passage  of  the  solvent  the  inflowing  current 
would  pass  along  the  walls  of  the  openings,  while  through 
the  central  channel  the  outflowing  current  would  be  located. 
When  the  thickness  of  the  solvent  layer  was  such  as  to  re- 
move the  particles  of  the  solute  a  distance  from  the  walls  of 
the  opening  in  the  membrane  greater  than  that  represented 
by  their  molecular  dimensions,  they  would  slip  through  and 
thus  pass  out  into  the  pure  solvent. 

Lhermite  (1854)  showed,  however,  that  if  a  layer  of  chloro- 
form be  placed  on  top  of  water  in  a  large  test  tube,  and  then 
ether  placed  on  top  of  the  chloroform  and  the  vessel  closed 
by  means  of  a  stopper  and  allowed  to  stand  for  a  day  or  two, 
there  would  be  only  two  liquid  layers.  The  ether  passes 
through  the  chloroform  and  appears  in  the  water  layer. 
That  is,  the  ether  dissolves  in  the  chloroform,  but  being  more 
soluble  in  water  it  is  extracted  by  the  water,  and  most  of  it 
appears  in  this  layer.  The  ether  is  distributed  between  the 
chloroform  and  the  water  layers  and  the  chloroform  is  the 
semipermeable  septum. 

Flusin  (1898-1900)  showed  that  by  using  vulcanized 
caoutchouc  as  the  semipermeable  membrane  and  employ- 
ing numerous  liquids  in  pairs  of  all  possible  combinations, 


OSMOTIC  PRESSURE  257 

the  main  current  was  from  the  liquid  which  is  the  more 
readily  absorbed  (imbibed)  by  the  rubber,  through  the 
membrane  into  the  liquid  less  readily  absorbed.  The  com- 
bination of  liquids  included  carbon  bisulphide,  chloroform, 
toluene,  benzene,  xylene,  benzyl  chloride,  turpentine,  nitroben- 
zene, ether,  methyl  alcohol,  ethyl  alcohol,  and  acetic  acid. 
By  using  as  the  membrane  hog's  bladder  and  having  ethyl 
alcohol  on  one  side,  he  placed  on  the  other  side  water,  methyl 
alcohol,  amyl  alcohol,  amyl  acetate,  chloroform,  benzene, 
and  many  others,  and  in  each  case  found  the  direction  of 
the  main  current  always  toward  the  ethyl  alcohol.  Raoult, 
by  employing  a  rubber  septum,  found  the  current  to  be  from 
ether  through  the  membrane  to  methyl  alcohol,  and  by  using 
hog's  bladder  as  septum  the  main  current  was  reversed. 

Kahlenberg  (1906)  by  employing  a  rubber  septum  has 
collected  a  large  amount  of  data  confirmatory  of  the  sol- 
vent action  of  the  semipermeable  membrane  and  concludes  : 
"  that  whether  osmosis  will  take  place  in  a  given  case  or  not 
depends  upon  the  specific  nature  of  the  septum  and  the 
liquids  that  bathe  it ;  and  if  osmosis  does  occur,  these  factors 
also  determine  the  direction  of  the  main  current  and  the 
magnitude  of  the  pressure  developed.  The  motive  power  in 
osmotic  processes  lies  in  the  specific  attractions  or  affinities 
between  the  liquids  used,  and  also  those  between  the  latter 
and  the  septum  employed." 

The  mechanism  of  osmosis  will  be  further  discussed  in 
Chapter  XXXV  on  Colloid  Chemistry. 

By  fastening  a  parchment  membrane  over  the  end  of  a 
thistle  tube,  filling  this  with  a  solution  of  cane  sugar,  and 
placing  the  bulb  of  the  tube  in  pure  water,  the  solvent  will 
pass  into  the  solution,  which  becomes  diluted.  The  passage 
of  the  water  into  the  solution  will  continue  until  the  hydro- 
static pressure  of  the  dilute  solution  in  the  tube  is  such  that  it 
prevents  any  more  of  the  water  from  going  through  the 
membrane  into  the  solution,  i.e.  the  tendency  of  the  water 


258  PHYSICAL   CHEMISTRY 

to  pass  in  is  balanced  by  this  hydrostatic  pressure,  and  the 
osmotic  cell  is  in  a  state  of  equilibrium.  The  pressure  thus 
developed  can  be  measured,  and  it  is  the  pressure  measured 
by  such  a  device  that  is  termed  the  osmotic  pressure  of  the 
solution.  This  pressure  is  also  conceived  to  be  due  to  the 
bombardment  of  the  membrane  by  the  molecules  of  the 
solute  present  in  the  solution,  and,  as  will  be  shown  later,  is 
considered  analogous  to  the  pressure  of  gaseous  molecules  on 
the  walls  of  the  containing  vessel. 

Precipitation  Membranes.  —  In  addition  to  the  numerous 
materials  that  have  been  given  as  examples  of  semipermeable 
membranes,  such  as  platinum,  palladium,  red-hot  iron,  vege- 
table membranes  (begonia  leaf),  animal  membranes  (blad- 
der), parchment  paper,  caoutchouc,  zeolites,  etc.,  there  is 
another  class  termed  precipitation  membranes,  which  are 
colloidal  gelatinous  precipitates  such  as  ferric  hydroxide, 
calcium  phosphate,  gelatine,  tannates,  etc. ;  but  the  one  most 
successfully  employed  is  copper  ferrocyanide,  discovered  by 
Traube. 

It  was  this  type  of  membrane  that  Pfeffer  (1877),  the 
botanist,  used  in  his  classic  experiments.  In  order  to  obtain 
a  strong  membrane  firmly  attached,  he  precipitated  the  mem- 
brane in  the  interstices  of  a  porous  unglazed  porcelain  cup. 
He  prepared  these  cells  by  soaking  them  first  in  water,  then 
in  a  three  per  cent  copper  sulphate  solution,  then  filling  the 
cell  with  a  three  per  cent  solution  of  potassium  ferrocyanide 
and  immersing  this  in  the  three  per  cent  copper  sulphate  solu- 
tion. The  solutions  diffuse  into  the  walls  of  the  cell,  where 
they  meet  with  the  formation  of  the  gelatinous  precipitate  of 
copper  ferrocyanide. 

2  CuSO4  +  K4FeCN6  =  Cu2FeCN6  +  2  K2SO4. 

After  standing  some  time  the  cell  is  removed  and  the  excess 
of  salts  carefully  washed  off.  It  is  essential  that  the  precipi- 
tate be  deposited  in  the  interstices  of  the  wall,  and  that  the 


OSMOTIC  PRESSURE 


259 


deposit  be  thin,  adherent,  and  absolutely  continuous.     These 
conditions  are  very  difficult  to  obtain. 

These  membranes  are  pervious  to  the  solvent  water  but  not 
to  the  dissolved  substances.  Pfeffer  found  that  when  these 
cells  containing  salt  solutions  were  immersed  in  pure  water, 
that  water  entered  through  the  semipermeable  wall  and 
diluted  the  solution.  The  tendency  of  the  water  to  dilute 
the  solution  was  measured  by  the  pressure  exerted  or  the 
height  to  which  the  liquid  would  rise  in  a  tube  against  the 
atmospheric  pressure  and  the  force  of  gravity.  Pfeffer  found 
that  these  pressures  against  the  walls  of  the 
membrane  were  enormous  —  amounting  to 
many  atmospheres. 

The  simple  device  Pfeffer  used  for  meas- 
uring these  pressures  is  illustrated  in  Fig.  80. 
It   consisted    of    an    unglazed   porcelain  cell, 
C,    in    the    interstices    of    which    the    copper 
ferrocyanide  membrane  was  precipitated.     To 
this    cell    was    attached    a    manometer,    M, 
by  means   of   which   the   pressures  could  be 
determined.       Table    XL    contains    Pfeffer's        FlG-  8o' 
data   and  illustrates  the   effect  of   concentration   on  this 
pressure,  which  is  termed  osmotic   pressure. 


TABLE  XL 


PER  CENT  CONCENTRATION, 
c 

OSMOTIC  PRESSURE  IN  CM.  HG., 
Po 

RATIO,  to 
c 

I 

53-8 

53-8 

I 

53-2 

53-2 

2 

101.6 

50.8 

2.74 

151.8 

554 

4 

208.0 

52.0 

6 

307.0 

5i-3 

i 

53-5 

53-5 

260  PHYSICAL   CHEMISTRY 

The  pressure,  p0,  which  is  expressed  in  centimeters  of 
mercury,    is    directly   proportional    to    the    concentration, 


The  effect  of  temperature  on  the  osmotic  pressure  of  sugar 
solutions  is  illustrated  by  the  data  in  Table  XLI. 

TABLE  XLI  —  SUGAR  AS  SOLUTE 


TEMP. 

P0  CM.  HG. 

6.8° 

50.5 

13-2 

52.1 

13-8 

52.2 

14.2 

53-1 

22.0 

54-8 

36.0 

56.7 

That  is,  the  osmotic  pressure,  pQ,  is  directly  proportional 
to  the  absolute  temperature. 

Van't  Hoff  from  a  consideration  of  Pfeffer's  data  saw  that, 
as  in  the  case  of  gases,  the  pressure  was  proportional  to  the 
concentration  (Boyle's  Law),  and  also  directly  proportional 
to  the  absolute  temperature  (Charles',  Gay  Lussac's  Law). 
Expressing  these  we  have 

P0  =  kcT  (i) 

The  concentration,  c,  Pfeffer  expressed  as  per  cent,  but  it 
can  be  expressed  in  any  way  we  choose,  as  we  have  previ- 
ously seen.  If  we  state  the  amount  of  solute,  g,  grams  in 

volume,  V,  then  c  =  — ,  or  for  n  gram-molecules  of  the  solute 
we  have  c  =  —.     Substituting  this  value  f or  c  in  (i)  we  have 

PO  ~    -y    >  ° 
P0V  =  nkT 


OSMOTIC   PRESSURE  261 

which,  when  n  —  i,  becomes 

p0V  =  kT.  (2) 

Van't  Hoff  recognized  this  as  similar  to  the  Gas  Law 
Equation  pV  =  RT  and  inquired  if  k  were  the  same  as  R. 
This  was  readily  ascertained  by  calculating  the  value  of  k 
from  Pfeffer's  data  as  follows  : 

A  one  per  cent  sugar  (C^H^Ou)  solution  at  13.8°  C.  gave 
an  osmotic  pressure  of  52.2  cm.  of  mercury. 

Since  pQV  =  nkT 

p  V 

solving  for  k  we  have  k  =  —^  —  . 

nT 

Substituting  in  this  equation  the  following  .values  :  pQ  = 
52.2  cm.  of  mercury,  or  710  grams  per  square  centimeter  ;  a 
one  per  cent  solution  contains  10  grams  per  liter  (assuming 
the  density  =  i)  ;  and  since  the  molecular  weight  of  sugar  is 
342,  we  have  ^£%  gram-molecules  in  i  liter,  or  1000  cc. 

•*•  n  =  -ST2  and  V  =  1000  cc. 
T  =  273°  +  13.8°  or  286.8° 
we  have 

T   _  710  X  looo  _  710  X  looo  X  342 
'      286.8  10  X  286.8 


or  k  =  84600  gram-centimeters  per  degree. 

But  R,  the  gas  constant,  equals  84,700  gram-centimeters 
per  degree,  and  van't  Hoff  concluded,  since  these  values  were 
experimentally  the  same,  that  k  =  R,  and  that  we  can  apply 
the  Gas  Law  Equation  to  solutions  in  which  the  osmotic  pres- 
sure of  a  dilute  solution  is  the  same  value  as  the  gaseous 
pressure  of  an  equivalent  mass  of  solute  would  be  at  the  same 
temperature,  and  occupying  the  volume  of  the  solution. 

This  application  of  The  Gas  Law  to  solutions  is  one  of  the 
great  contributions  of  van't  Hoff  to  the  development  of 
chemistry. 


262 


PHYSICAL   CHEMISTRY 


OSMOTIC  PRESSURE  OF  SOLUTIONS 

Confirmatory  data  have  been  published  by  numerous 
workers,  including  Ladenburg,  Adie,  Tammann,  Ponsot,  and 
particularly  Naccari  (1897),  whose  results  are  among  the 
few  marked  duplications  of  Pfeffer's  work.  A  four  per  cent 
glucose  solution  at  o°  C.  should  give  an  osmotic  pressure  of 
37.6  cm.,  and  Naccari  found  the  following  values.:  37.0, 
37.8,  37.8.  For  a  four  per  cent  mannite  solution  the  calcu- 
lated value  is  38.3  cm.  at  o°,  and  Naccari  found  37.3,  37.6, 
37-9,  37-5,  37-5,  36.3,  3^-4,  which  is  an  excellent  agreement. 

More  recently,  however,  we  have  the  excellent  work  of 
Morse  and  his  collaborators  (1908-13).  This  shows  a  marked 
confirmation  of  van't  Hoff's  generalization,  as  Table  XLII 
illustrates. 

TABLE  XLII 

Ratio  of  observed  osmotic  pressure  to  calculated  gas  pressure  at  the 
same  temperature,  the  volume  of  the  gas  being  that  of  the  solvent  in 
the  pure  state. 


CANE  SUGAR 

GLUCOSE 

WEIGHT  NORMAL 
CONCENTRATION 

Series  I 

Series  II 

Series  I 

Temperature 

Ratio 

Tempera- 
ture 

Ratio 

Tempera- 
ture 

Ratio 

O.I 

18.71° 

I.OI7 

24-23° 

1.049 

25.10° 

0.996 

0.2 

20.91 

0.998 

21.38 

0.996 

24-93 

0.981 

0-3 

19.28 

1.  001 

21.67 

1.004 

22.20 

0.986 

0-5 

20.84 

0-993 

22.67 

1.  000 

21.86 

1.003 

0.7 

20.14 

0-993 

23.64 

1.  000 

22.26 

0.998 

0.8 

19.56 

I.OI2 

23.69 

1  .002 

23.28 

0.991 

0.9. 

19.84 

1.  006 

24.79 

0.998 

23.80 

0-993 

I.O 

23.32 

I.OI2 

23.56 

I.OIO 

22.20 

1.002 

The  value  of  the  ratios  in  this  table  is  approximately  unity, 
and  Morse  concludes  from  his  results  :  "  That  in  the  vicinity 
of  20°  the  osmotic  pressure  exerted  by  both  cane  sugar  and 
glucose  is  equal  to  that  which  a  molecular  equivalent  quantity 


OSMOTIC  PRESSURE  263 

of  a  gas  would  exert  if  its  volume  were  reduced,  at  the  same 
temperature,  to  the  volume  of  the  solvent  in  the  pure  state." 

Lord  Berkeley  and  E.  G.  J.  Hartley  (1906),  instead  of 
measuring  the  pressure  developed  in  an  osmotic  cell  by  the 
passage  of  the  solvent  into  the  cell,  as  is  usually  done,  sepa- 
rated the  solution  from  the  solvent  by  a  semipermeable 
membrane  and  then  subjected  the  solution  to  a  gradually 
increasing  pressure  until  the  solvent  which  first  flowed  into 
the  solution  reversed  its  direction  and  flowed  out.  The 
pressure,  which  was  just  sufficient  to  produce  this  reversal 
of  the  current  and  to  prevent  the  solvent  from  flowing  into 
the  solution,  was  taken  as  the  equivalent  of  the  osmotic  pres- 
sure of  the  solution. 

By  this  new  dynamic  method  Lord  Berkeley  and  Hartley 
determined  the  osmotic  pressure  by  measuring  the  rate  of 
flow  of  the  solvent  into  the  solution.  By  assuming  that  this 
rate  of  flow  is  the  same  as  that  which  would  occur  if  the  sol- 
vent were  caused  to  pass  through  the  semipermeable  mem- 
brane under  a  mechanical  pressure  equal  to  the  osmotic 
pressure  of  the  solution,  they  find  that  if  only  the  initial  rate 
of  flow  is  considered,  the  values  for  the  osmotic  pressure, 
in  the  case  of  dilute  solutions,  agree  well  with  those  obtained 
by  the  direct  measurement.  In  concentrated  solutions  the 
discrepancy  is  greater  than  by  the  other  method,  yet  it  may 
have  wide  application. 

De  Vries,  the  botanist,  worked  on  the  osmotic  pressure  of 
plant  cells.  He  found  that  if  a  plant  cell  is  placed  in  a 
strong  sugar  solution  the  cell  will  shrink,  while  in  a  weak 
solution  it  will  swell  up.  By  the  introduction  of  a  cell  into 
other  solutions  the  same  results  were  obtained.  The  cell 
wall  is  permeable  to  water  and  impervious  to  the  dissolved 
substances. 

De  Vries  determined  the  strength  of  various  solutions  that 
caused  the  plant  cell  wall  to  be  just  separated  from  the  proto- 
plasm. This  process  of  the  separation  is  designated  plas- 


•  '  . 
264  PHYSICAL   CHEMISTRY 

molysis,  and  the  cell  is  said  to  be  plasmolyzed.  Those  solu- 
tions of  the  strength  just  sufficient  to  produce  plasmolysis  are 
equal  in  osmotic  action.  Solutions,  such  as  these,  which  have 
the  same  osmotic  pressure,  contain  equimolecular  quantities 
of  the  dissolved  substances  and  are  called  isotonic  solutions. 
These  results  are  designated  as  normal ;  but  another  class  of 
compounds  gave  values  for  the  plasmolysis  that  were  abnor- 
mal, and  the  osmotic  pressure  values  for  these  solutions  were 
likewise  abnormal.  The  binary  substances  (uni-univalent) 
such  as  KNO3,  NaCl,  KBr,  KQjHsC^,  etc.,  gave  practically 
twice  the  osmotic  action  they  should  have  from  the  gram- 
molecular  content  of  the  solution.  Salts  (uni-bivalent)  of 
diacid  bases  and  of  dibasic  acids  gave  values  approximately 
three  times  what  they  should  have. 

Hamburger  obtained,  with  red  blood  corpuscles,  results 
which  were  in  accord  with  the  other  animal  and  vegetable 
organisms  employed  as  semipermeable  membranes. 

Hence  in  dilute  solutions  of  different  substances  we  find 
that  the  osmotic  pressure  conforms  to  all  the  gas  laws,  being 
proportional  to  the  concentration,  that  is,  inversely  propor- 
tional to  the  volume  (Boyle's  Law) ;  the  coefficient  of  varia- 
tion of  the  pressure  with  the  temperature  is  the  same  for  all 
substances  (Gay  Lussac's  Law) ;  equimolecular  solutions 
have  the  same  osmotic  pressure,  or  conversely,  solutions  that 
have  the  same  osmotic  pressure  contain  the  same  number 
of  moles  in  a  given  volume  (Avogadro's  Law). 

The  absolute  value  of  the  osmotic  pressure  is  the  same  as 
the  gaseous  pressure  of  the  dissolved  substance  would  be  if 
we  could  allow  it  to  remain  at  the  same  temperature  and 
occupy  the  volume  of  the  solution  but  remove  the  solvent. 

The  laws  of  gases  we  have  seen  hold  only  for  ideal  gases ; 
so  too  we  shall  see  that  the  application  of  these  to  solutions 
holds  only  for  ideal  solutions,  but  in  the  case  of  dilute  solu- 
tions the  variations  are  not  so  pronounced  as  in  more  con- 
centrated solutions. 


CHAPTER  XXIV 
LOWERING  OF  VAPOR  PRESSURE 

IN  the  discussion  of  one  and  two  component  systems  it 
will  be  recalled  that  the  vapor  pressures  of  these  systems  were 
represented  on  pt  diagrams.  In  Fig.  8 1  we  may  represent  the 
vapor  pressure  on  the  vertical  axis  and  the  f 
temperature  on  the  horizontal  axis.  Then 
the  vapor  pressure  of  the  system  water  may 
be  represented  by  the  following  curves : 
=  the  vaporization  curve. 


CD  =  the  sublimation  curve.  t 


_  .         .,,      r     •  FIG.  81. 

CA  —  the  fusion  curve. 

As  a  second  component  (a  nonvolatile  solute)  is  added,  the 
vapor  pressure  of  the  solvent  is  lowered,  and  for  a  specified 
concentration  the  vapor  pressure  of  the  solution  would  be 
represented  by  the  curve  EF.  At  a  specified  temperature,  t, 
the  vapor  pressure  of  the  solvent  has  been  lowered  by  the 
addition  of  the  solute  from  p  to  pi.  That  is,  at  the  tempera- 
ture t  the  vapor  pressure  of  the  solvent  pi  is  equal  to  Bt, 
and  the  vapor  pressure  of  the  solution  at  the  same  tempera- 
ture t  is  Ht,  then  the  vapor  pressure  has  been  lowered  p  —  pi 
or  BH.  At  any  other  temperature,  t\,  the  lowering  of  the 
vapor  pressure  is  I K  or  p2  —  ps.  The  ratio  of  the  lowering  to 

.    _      .  T2TT 

the  original  vapor  pressure  of  the  pure  solvent  is  *- ^  =  -=— 

p  Bt 

T  IS"  jj      tj 

and  j^-  =  ™ £-3.     But  von  Babo  showed  that  the  ratio 

of  the  lowering  of  the  vapor  pressure  of  the  solvent  to  the 
vapor  pressure  of  the  pure  solvent  is  not  a  function  of  the 
temperature,  hence 

265 


266 


PHYSICAL   CHEMISTRY 


IK  ^pz  -  p3 


therefore 


We  have  seen  that  the  amount  of  lowering  of  the  vapor 
pressure  of  the  solvent  is  proportional  to  the  concentration. 
This  is  known  as  Wullner's  Law,  which  is  expressed  as  follows  : 
The  ratio  of  the  change  in  the  vapor  pressure  of  the  solvent 
to  the  vapor  pressure  of  the  solvent  is  proportional  to  the  con- 
centration, i.e. 


If  we  express  the  concentration  in  terms  of  the  number 
of  moles  of  the  solvent  and  of  the  solute,  we  have 
P  -  Pi  =  kn_ 
p  N 

in  which  n  =  the  number  of  moles  of  the  solute  and  N  the  num- 
ber of  moles  of  the  solvent.     This  is  known  as  Raoult's  Law. 

Employing  ether  as  a  solvent,  Raoult  showed  that  the  ratio 
of  the  vapor  pressures  of  solvent  and  solution  is  independent 
of  the  temperature,  which  is  a  confirmation  of  von  Babo's 
Law.  This  is  evident  from  Table  XLIII. 

TABLE  XLIII 

(After  Jones) 


16.482  GRAMS  OIL  OF  TURPENTINE  IN  too 

10.442  GRAMS  ANILINE   IN   100  GRAMS 

GRAMS  OF  ETHER 

ETHER 

Vapor  Pressure 

Ratio 

Vapor  Pressure 

Ratio 

ture 

of  Solvent  p 

of  Solu- 
tion pi 

I-'XIOQ 

ature 

of  Solvent  p 

of  Solu- 
tion pi 

Jxioo 

1.1° 

199.0 

I88.I 

91-5 

1.1° 

199-5 

183.3 

91.9 

3-6 

224.0 

204.7 

91.4 

3-6 

223.2 

204.5 

91.6 

18.2 

408.5 

368.7 

9I.O 

9-9 

289.1 

264.0 

91-3 

21.8 

472.3 

430.7 

91.2 

21.8 

472.9 

432.7 

91-5 

LOWERING  OF  VAPOR  PRESSURE 


267 


Raoult  selected  a  number  of  substances  with  a  low  vapor 
pressure,  such  as  oil  of  turpentine,  aniline,  nitrobenzene, 
ethyl  salicylate,  etc.,  the  boiling  points  of  which  ranged 
between  160°  and  222°,  and  dissolved  these  in  ether,  which 
has  a  high  vapor  pressure  as  compared  with  the  solutes.  In 
Table  XLIV  are  given  the  solutes,  the  molecular  weights,  n,  the 

number  of  moles  of  the  solutes,  ^ ft ,  the  ratio  of  the  change 

P 

in  the  vapor  pressure  of  the  solvent,  caused  by  addition  of 
the  solute,  to  the  vapor  pressure  of  the  solvent,  i.e.  the 
fractional  lowering  of  the  vapor  pressure,  and  in  the  next 


column, 


np 


the  fractional  lowering  produced  by  one 


mole  when  dissolved  in  100  moles  of  ether.  K  is  the  molar 
lowering  of  the  vapor  pressure  when  100  grams  of  the  solvent 
are  employed. 

TABLE  XLIV 


SOLUTES 

MOLECULAR 
WEIGHT 

n 

p-pi 
P 

P-pi 
np 

K 

Turpentine 

1  16 

8  95 

o  0885 

o  0099 

O  71 

Methyl  salicylate    .     .     . 
Methyl  benzoate 
Benzoic  acid  

152 
136 
122 

2.91 
9.60 

7-175 

0.026 
0.091 
0.070 

O.OO89 
0.0095 
O.OOQ7 

0.71 
0.70 
O.7I 

Trichloracetic  acid  .     .     . 
Caprylic  alcohol 
Aniline 

163.5 
130 

Q7 

11.41 
6.27 
766 

0.120 

o  08  1 

O.OIO5 
O.OIIO 

o  0106 

0.71 

0-73 

O  71 

Cyanic  acid    .          .     .     . 
Benzaldehyde     .... 
Cyanamide 

43 
106 
42 

O.7O 
0.72 

O  7  A 

Antimony  trichloride  . 
Carbon  hexachloride    .     . 

228.5 
237 

0.0087 

0.0100 

0.71 
0.71 

From  Raoult's  Law  *- ^  —  k — ,  we  have 

p  N  np          N, 

which  is  the  value  given  in  the  next  to  the  last  column.     The 
mean  value  of  fourteen  substances  employed  by  Raoult  was 


268 


PHYSICAL   CHEMISTRY 


0.0098,  which  is  practically  o.oi,  that  is,  one  mole  of  any  sub- 
stance dissolved  in  100  moles  of  the  solvent  (ether)  lowers  the 
vapor  pressure  of  the  solvent  one  one-hundredth  of  its  value. 

And  since  N  =  100  and  2 ^  =  o.oi,  we  have  on  substi- 

np 

k 

tution   o.oi  =  —    or    i  =  k.      That   is,   the   constant   of 
100 

Raoult's  Law  is  unity  for  ether,  and  so  the  expression  for  the 

law  becomes  f  ~  ?l  =  -^-  in  general.     From  the  data  pre- 

p  N 

sented  in  Table  XLV  the  mean  value  of  the  constant  for  a  large 
number  of  solvents  is  0.0105,  which  is  virtually  one  one- 
hundredth.  Therefore,  one  mole  of  a  nonvolatile  substance 

TABLE  XLV 

(After  Jones) 


SOLVENTS 

MOL.  WEIGHT 

K 

K 
M 

Water      
Phosphorus  trichloride  . 
Carbon  bisulphide     .... 
Tetrachlor  methane  .     .     .  •  . 
Chloroform 

18 
137-5 
76 
154 
II9-5 
70 
78 
142 
109 

74 
58 
32 
A^ 

0.185 
1.49 
0.80 
1.62 
1.30 
0.74 
0.83 
1.49 
1.18 
0.71 
0-59 
0-33 
/erage  value 

0.0102 
0.0108 
O.OIO5 
0.0105 
0.0109 
0.0106 
O.OIO6 
O.OIO5 
0.0109 
0.0096 
O.OIOI 
O.OIO3 
0.0105 

Amylene  
Benzene  *••".- 
Methyl  iodide  
Ethyl  bromide 

Ether 

Acetone  .  .... 

Methyl  alcohol  

dissolved  in  100  moles  of  any  volatile  liquid  lowers  the  vapor 
pressure  of  this  liquid  by  a  nearly  constant  fraction  approxi- 
mately o.oi  of  its  value.  We  are  therefore  justified  in 

expressing  Raoult's  Law  thus,  * —  =  -^,    remembering 


that  the  proportionality  factor  is  unity. 


LOWERING  OF  VAPOR   PRESSURE  269 

For  concentrated  solutions,  in  the  equation  £ ^  =  -^- , 

p          N 

the  right-hand  member  may  become  —  =  i ,  when  the  solu- 
tion is  so  concentrated  that  the  number  of  moles  (n)  of  the 
solute  is  equal  to  the  number  of  moles  ( N)  of  the  solvent. 

Then  ^ "  =  i ,   and  this  may   be  written  £  —  O  =  i , 

P  P      P 

which  becomes  ^  =  o,  which  is  an  impossibility,  for  the 

P 

vapor  pressure  of  a  concentrated  solution  will  always  have 
some  numerical  value.  Raoult  therefore  changed  the  for- 
mula to  read  *- &  =  n — • ,  which  expresses  the  ratio  of 

p  N  +  n 

the  number  of  moles  of  the  solute  to  the  total  number  of  moles 
present,  and  this  holds  for  concentrated  solutions. 

If  we  obtain  the  relative  lowering  of  the  vapor  pressure  of 

£ —  when  we  have  a  specified  weight,  g,  of  the  solute  dis- 

P 

solved  in  a  constant  quantity  of  the  solvent,  then  P  ~  P1 

gP 

is  the  relative  lowering  for  one  gram  of  solute,  and  ^  ~  Pv  m 

gP 

is  the  lowering  for  one  mole  of  the  solute.     That  is,  ^  ~  P1'  m 

& 

is  the  fractional  molecular  lowering  of  the  vapor  pressure. 
Values  of  K  for  100  grams  of  the  solvent  are  given  in  Table 
XLV. 

The  lowering  of  the  vapor  pressure  can  be  utilized  as  a 
means  for  the  determination  of  the  molecular  weight  of  sub- 
stances. By  definition 

n  —  •£-,  in  which  g  is  the  grams  of  the  solute 
m 

and  m  the  molecular  weight, 


270  PHYSICAL   CHEMISTRY 

and  N  =  —  .in  which  5  is  the  grams  of  the  solvent 

M 

and  M  is  its  molecular  weight. 

Substituting  in  the  modified  Raoult  formula,  which  is 

P  -  Pi  =       n 
p  N  +  n 

JL 

p  —  pi          m 
we  have  L *-*  =  -r; • 

P  £+1 

M     m 

This  equation  may  be  used  for  calculating  the  molecular 
weight  of  the  solute,  or  if  this  is  known,  'the  vapor  pressure, 
pi,  of  the  solution  can  be  ascertained  providing  the  other 
terms  of  the  equation  are  known. 

RELATION  OF  THE  LOWERING  OF  THE  VAPOR  PRESSURE  TO 
OSMOTIC  PRESSURE 

The  vapor  pressure  of  a  solution  is  intimately  related 
to  the  osmotic  pressure  of  the  solution.  Suppose  that  an 
aqueous  solution  of  a  nonvolatile  solute  and  the  pure  water 
be  placed  in  separate  vessels  under  a  bell  jar  and  the  air 
exhausted  until  the  liquids  are  virtually  under  the  pressure 
of  the  vapor  of  the  pure  solvent.  Since  the  vapor  pressure 
of  the  solution  is  less  than  that  of  the  pure  solvent,  dis- 
tillation will  take  place  from  the  pure  solvent  to  the  solution, 
where  condensation  will  occur  with  an  increase  in  the  volume 
of  the  solution  and  a  resulting  decrease  in  the  volume  of  the 
solvent.  By  keeping  the  solution  stirred,  the  dilution  will 
continue  until  the  liquids  are  in  equilibrium  with  the  vapor 
directly  above  and  in  contact  with  them. 

If  we  have  two  isotonic  solutions,  A  and  B,  separated  by 
a  semipermeable  membrane  and  contained  in  an  inclosed 
vessel,  and  if  the  saturated  vapor  above  the  solutions  be  not 


LOWERING  OF  VAPOR  PRESSURE 


271 


the  same,  there  will  be  a  passage  of  the  vapor  from  the  one 
solution,  A,  to  the  other,  B,  resulting  in  the  dilution  of  B 
and  a  corresponding  concentration  of  A.  This  change  in 
concentration  would  cause  the  passage  of  the  solvent  through 
the  semipermeable  membrane  from  B  to  A,  which  would  re- 
sult in  the  production  of  a  condition  for  a  perpetual  motion. 
It  therefore  follows  that  in  the  case  of  isotonic  solutions  the 
vapor  pressures  are  equal. 

By  a  simple  proof  Arrhenius  has  shown  the  relation  between 
the  vapor  pressure  and  osmotic  pressure  without  the  use  of 
thermodynamics . 

In  Fig.  82  is  illustrated  an  osmotic  pressure  cell  in  which 
the  solution  within  the  cell  has  come  to  rest  at  the  height  h, 
and  all  is  inclosed  under  the  bell  jar  from  which  the  air  has 
been  removed,  leaving  the  system  under  the 
pressure  of  the  vapor  of  the  pure  solvent. 
At  equilibrium  the  solvent  does  not  pass  by 
distillation  either  into  the  solution  or  out  of 
it.  But  the  vapor  pressure,  p,  of  the  sol- 
vent is  greater  than  the  vapor  pressure,  pi, 
of  the  solution  by  the  weight  of  the  column 
of  vapor  represented  by  the  difference  be- 
tween the  height  h  of  the  two  surfaces. 
Therefore,  the  vapor  pressure  of  the 
solution  must  be  less  than  the  vapor  pressure  of  the  pure 
solvent  by  the  amount  equivalent  to  the  weight  of  the  column 
of  vapor  of  unit  area  of  the  height  h.  That  is, 

if  p  =  vapor  pressure  of  solvent 

pi  =  vapor  pressure  of  solution 
h  =  height  of  the  osmotic  column 
P  =  density  of  the  vapor  of  solvent 

then  p  —  pi  =  hp.  (i) 

The  osmotic  pressure  of  the  solution  is  equivalent  to  the 
weight  of  the  column  of  the  solution  per  unit  area  of  the  height 


FIG.  82. 


272  PHYSICAL   CHEMISTRY 

h.  Hence  the  change  in  the  vapor  pressure  is  to  the  osmotic 
pressure  as  the  weight  of  any  volume  of  vapor  is  to  the  weight 
of  the  same  volume  of  the  liquid,  which  gives 


in  which  pi  is  the  density  of  the  solution.     Now,  since  p  = 
—  -,  substituting  in  the  Gas  Law  Equation,  pV  =  nRT,  we 


have  p  =  ^—-  .     Similarly,  since  pi  =  -f-,  in  which  g  is  the 
Kl  V 

weight  of  the  solution  and   V  its  volume,  substituting  in 
van't  Hoff's  equation  for  osmotic  pressure,  p°V  =  nRT,  we 


have  pi  =  -.     Then      =  .     Substituting  this  value 

nRT  PI       p0g 

in  equation  (2)  we  have  p  —  pi  =  ^  —  .     As  g  is  the  weight 

g 

of  the  solvent  (of  an  infinitely  dilute  solution)  and  M  the 
molecular  weight  as  determined  from  the  vapor  density  (no 
assumption  is  made  concerning  its  molecular  weight  in  the 

liquid  state)  ,  —  =  —  ,  the  reciprocal  of  the  number  of  moles 

g      N 

of  the  solute.     The  equation  then  takes  the  form 

>:*-? 

which  is  Raoulfs  Law. 


CHAPTER  XXV 


FIG.  83. 


FREEZING    POINTS  AND    BOILING  POINTS   OF    SOLUTIONS 

IT  will  be  recalled  that  the  freezing  point  is  the  tempera- 
ture at  which  the  three  phases  —  solid,  liquid,  and  vapor  — 
are  in  equilibrium,  and  is  represented  by  A  in  Fig.  83.  On 
the  pt  diagram,  A  B  is  the  vapor 
pressure  curve  of  pure  water,  and  ' 
AC  is  the  sublimation  curve.  The 
intersection,  A,  is  the  triple  point 
and  represents  the  temperature  and  ^ 
pressure  at  which  the  three  phases 
—  ice,  liquid,  and  vapor  —  are  in 
equilibrium.  The  pressure  is,  how- 
ever, the  vapor  pressure  of  the  pure 
substance  and  is,  as  we  have  previ- 
ously seen,  4.6mm.,  while  the  temperature  is  not  o°  C.,  since 
the  freezing  point  is  designated  as  the  temperature  of  equilib- 
rium under  atmospheric  pressure.  The  freezing  point  is  then 
not  quite  the  same  as  the  triple  point  A,  but  at  760  mm.  pres- 
sure differs  from  it  slightly,  the  freezing  point  being  0.0075° 
lower  than  the  transition  point.  As  the  change  for  one  atmos- 
phere pressure  is  small,  for  a  few  millimeters  difference  in 
pressure  the  differences  are  negligible,  and  no  serious  error 
is  introduced  in  practice-if  we  consider  the  two  points  identical, 
remembering,  however,  that  to  obtain  the  true  transition 
point  correction  for  the  pressure  must  be  made. 

For  the  solution,  the  vapor  pressure  is  lower  than  the 
vapor  pressure  of  the  pure  solvent,  and  at  some  specified 
concentration  we  shall  assume  that  the  line  CE  represents 
the  vapor  pressure  of  the  solution.  The  intersection,  C,  of 

273 


ff 


274  PHYSICAL  CHEMISTRY 

the  vapor  pressure  curve,  CE,  of  the  solution,  and  the  subli- 
mation curve,  AC,  represents  the  equilibrium  between  ice, 
solution,  and  vapor,  and  is  the  freezing  point  of  the  solution. 
The  freezing  point  then  has  been  lowered  from  the  tempera- 
ture /i,  to  the  temperature  k,  i-e-  the  lowering  of  the  freezing 
point  is  /i  —  /2,  and  at  the  same  time  the  vapor  pressure  has 
been  lowered  from  pi,  that  of  the  pure  solvent,  to  p%,  the  vapor 
pressure  of  the  solution,  or  pi  —  pz. 

It  is  therefore  apparent  that  the  lowering  of  the  freezing 
point  bears  an  intimate  relation  to  the  lowering  of  the  vapor 
pressure  of  solutions,  and  there  must  be  a  way  of  expressing 
this  lowering  of  the  freezing  point  in  terms  of  the  lowering 
of  the  vapor  pressure  of  the  solvent. 

It  should  be  remembered  that  we  are  assuming  that  the 
solid  phase  separating  from  the  solution  is  pure  solvent,  other- 
wise we  might  get  a  rise  of  the  freezing  point,  as  in  the  case 
where  solid  solutions  or  isomorphous  mixtures  are  separated 
out.  In  the  case  of  the  separation  of  eutectic  mixtures  the 
simple  relation  will  not  hold. 

As  early  as  1788  Blagden  showed  that  the  freezing  points  of 
aqueous  solutions  of  a  given  substance  are  lower  than  that 
of  the  pure  substance,  and  that  this  lowering  of  the  freezing 
point  is  proportional  to  the  concentration.  But  it  was  not 
until  the  work  of  Rudorff  (1861)  and  of  Coppet  (1871)  that 
attention  was  given  to  the  freezing  point  of  solutions.  It 
was,  however,  the  work  of  Raoult,  published  in  1882,  that 
presented  the  fundamental  facts.  He  showed  that  the  low- 
ering of  the  freezing  point  is  proportional  to  the  concentra- 
tion, and  that  the  lowering  of  the  freezing  point  of  solutions 
for  various  solutes  is  nearly  the  same  when  one  mole  of  the 
solutes  is  dissolved  in  the  same  amount  of  the  solvent.  He 
found  that  this  is  true  not  only  for  water  but  also  for  a  large 
number  of  organic  solvents  as  well.  This  is  illustrated  in 
Table  XL VI,  which  contains  some  of  Raoult 's  extensive  data. 
The  molecular  lowering  represents  the  lowering  of  the  freez- 


FREEZING  POINTS  AND   BOILING  POINTS 


275 


ing  point  produced  by  one  mole  of  solute  dissolved  in  100 
grams  of  the  solvent. 

TABLE  XLVI 
Solvent :     Water 


SOLUTE 

MOLECULAR 
LOWERING  IN 
DEGREES  C. 

SOLUTE 

MOLECULAR 
LOWERING  IN 
DEGREES  C. 

Acetamide    .... 

I7.8 

Hydrochloric  acid   .     . 

39-1 

Acetic  acid   .... 

19.0 

Nitric  acid     .... 

35-8 

Aniline     

15-3 

Sulphuric  acid    . 

38.2 

Cane  sugar  .... 

18-5 

Potassium  hydroxide  . 

35-3 

Ether  

16.6 

Sodium  hydroxide 

36.2 

Ethyl  alcohol    .     .     . 

17-3 

Barium  chloride 

48.6 

Ethyl  acetate    .     .     . 

17.8 

Calcium  chloride 

49-9 

Glycerine      .... 

17.1 

Potassium  chloride 

33-6 

Phenol     

15-5 

Sodium  chloride      .     . 

35-i 

Urea 

17  2 

Potassium  nitrate 

10  8 

/ 

^V-J.O 

Solvent :     Benzene 


SOLUTE 

MOLECULAR 
LOWERING  IN 
DEGREES  C. 

SOLUTE 

MOLECULAR 
LOWERING  IN 
DEGREES  C. 

Anthracene  .... 
Aniline 

Si-2 
4.6  ^ 

Acetic  acid  .... 
Benzoic  acid 

25-3 

2^  A. 

Carbon  disulphide 
Chloral     .     .     . 

49-7 

co  1 

Amyl  alcohol  .  .  . 
Ethyl  alcohol 

39-7 

28  2 

Chloroform  .... 
Ether  

5i-i 

4Q.7 

Methyl  alcohol  .  .  . 
Phenol  .  .  . 

25-3 
-\2  d. 

Methyl  iodide  . 
Naphthalene     .     .     . 
Nitrobenzene     .     ... 
Nitroglycerine  . 

50.4 
50.0 
48.0 
49-9 

Solvent :     Nitrobenzene 


MOLECULAR 

MOLECULAR 

SOLUTE 

LOWERING  TN 

SOLUTE 

LOWERING  IN 

DEGREES  C. 

DEGREES  C. 

Benzene  .     .     .     .     . 

70.6 

Acetic  acid     .... 

36.1 

Chloroform  .     .     .     . 

69.9 

Benzoic  acid  .... 

37-7 

Ether  

67.4 

Ethyl  alcohol      .     .     . 

35-6 

Stannous  chloride  .     . 

71.4 

Methyl  alcohol  .     .     . 

35-4 

276 


PHYSICAL   CHEMISTRY 


Solvent :     Acetic  Acid 


SOLUTE 

MOLECULAR 
LOWERING  IN 
DEGREES  C. 

SOLUTE 

MOLECULAR 
LOWERING  IN 
DEGREES  C. 

Benzoic  acid 

43-0 

Hydrochloric  acid  .     . 

17.2 

Chloroform  .... 

38.6 

Sulphuric  acid    .     .     . 

18.6 

Chloral                    .     . 

•70   2 

Magnesium  acetate 

18  2 

Ether                       .     . 

T.Q  A 

Ethylene  chloride  .     . 

4O.O 

Ethyl  alcohol    .     .     . 

36.4 

Glycerine           .     .     , 

36.2 

Nitrobenzene     .     .     . 

41.0 

Stannic  chloride    .     . 

41-3 

Water      

33-0 

From  the  above  tables  it  will  be  observed  that  the  sub- 
stances on  the  left  hand  give  for  the  same  solvent  approxi- 
mately the  same  molecular  lowering  of  the  freezing  point. 
In  the  case  of  water  the  solutes  listed  in  the  right-hand  side 
of  the  table  give  molecular  lowerings  approximately  twice, 
in  some  cases  three  times,  as  great  as  the  normal  values  listed 
in  the  other  column  of  the  table.  These  abnormally  high 
values  for  the  molecular  lowering  are  attributed  to  the  dis- 
sociation of  the  solute,  analogous  to  the  abnormal  values  of 
the  density  of  certain  vapors  which  we  attribute  to  the  in- 
creased number  of  parts  or  molecules  resulting  from  the 
dissociation  of  the  substance.  We  shall  refer  to  this  type 
of  abnormal  values  later  for  a  full  discussion.  In  the  case  of 
benzene,  nitrobenzene,  and  acetic  acid,  when  used  as  solvents, 
we  observe  that  the  values  for  the  molecular  lowering  in  the 
left-hand  column  are  approximately  twice  the  values  in  the 
right-hand  column.  The  normal  values  are  considered  to  be 
those  in  the  left-hand  column,  while  the  smaller  values  are 
designated  the  abnormal  values,  and  these  abnormally  small 
lowerings  are  explained  upon  the  basis  of  the  association  of 
some  of  the  solute  molecules.  The  lowering  of  the  freezing 
point  is  proportional  to  the  number  of  dissolved  molecules, 


FREEZING  POINTS   AND   BOILING  POINTS  277 

and  as  shown  from  the  values  given  in  the  above  table,  it  is 
independent  of  their  nature.  We  have  previously  seen  that 
some  substances  in  the  liquid  state  have  molecules  which  are 
aggregates  of  the  molecules  of  the  substance  when  it  is  in  the 
gaseous  state,  i.e.  they  are  said  to  be  associated.  These 
abnormal  values  of  the  molecular  lowering  can  be  accounted 
for  by  assuming  that  there  is  a  decrease  in  the  number  of 
molecules  of  the  solute  due  to  association,  while  in  the  case 
of  some  solutes  in  water  the  increase  in  the  number  of  mole- 
cules of  the  solute  is  due  to  the  dissociation  of  the  solute 
molecules. 

MOLECULAR  WEIGHT  DETERMINATIONS 

Freezing  Point  Method.  —  Let 

g  =  the  number  of  grams  of  solute 
m  =  the  molecular  weight  in  grams  of  solute 
5  =  the  weight  in  grams  of  the  solvent 
A  =  the  lowering  of  the  freezing  point  produced  by  g 

grams  of  solute  in  5  grams  of  solvent. 
Then 

-  =  lowering  of  freezing  point  produced  by  one  gram  of 

solute  in  5  grams  of  solvent. 

-  =  lowering  of  freezing  point  produced  by  one  gram  of 

o 

solute  in  one  gram  of  the  solvent. 

-  =  lowering  of  freezing  point  produced  by  one  mole  of 

8 

solute  in  one  gram  of  the  solvent,  i.e.  the  mo- 
lecular lowering. 

-  is  the  molecular  lowering  for  100  grams  of  the  solvent. 
100  g 

But  we  saw  that  for  a  specified  solvent  the  molecular  lowering 
is  constant,  hence  we  have 


100  g 


278  PHYSICAL   CHEMISTRY 

And  solving  for  m  we  have 


in  which  Kpg  is  the  molecular  lowering  when  one  mole  is  dis- 
solved in  100  grams  of  solvent;  then  100  KF  would  be  the 
molecular  lowering  when  one  mole  is  dissolved  in  one  gram 
of  solvent. 

From  this  equation  we  have  a  method  for  calculating  the 
molecular  weight  of  a  substance  from  the  freezing  point 
lowering,  for  it  is  only  necessary  to  determine  A,  the  lowering 
produced  when  g  grams  of  solute  are  dissolved  in  5  grams  of 
the  solvent,  and  the  constant  Kp  is  known  for  the  solvent. 

We  have  seen  that  Raoult  determined  the  value  for  Kp  ex- 
perimentally. Subsequently  a  very  large  amount  of  work 
has  been  done  in  order  to  obtain  this  value  with  a  high  degree 
of  accuracy.  Nernst  and  Abegg  discussed  the  theory  of  the 
freezing  point  determinations,  and  Beckmann  has  devised 
the  common  form  of  apparatus  employed  in  these  determina- 
tions. We  define  the  freezing  point  as  the  temperature  at 
which  the  liquid  and  solid  solvent  are  in  equilibrium  at  at- 
mospheric pressure. 

In  Beckmann's  apparatus,  Fig.  84,  we  have  an  inner  vessel, 
in  which  a  thermometer  and  a  stirrer  are  placed,  containing 
an  isolated  mass  of  liquid  to  be  frozen.  This  is  surrounded 
by  another  tube  forming  an  air  jacket,  which  in  turn  is  sur- 
rounded by  the  freezing  mixture.  In  this  determination  it 
is  assumed  that  when  the  liquid  freezes  a  small  quantity  of 
ice  is  formed,  and  this  is  in  equilibrium  with  the  liquid  at  a 
fixed  temperature,  which  is  taken  as  the  true  freezing  point 
of  the  liquid.  But  as  Nernst  and  Abegg  have  shown,  this 
isolated  mass  of  liquid  and  ice  is  at  a  higher  temperature  than 
the  surrounding  freezing  mixture  and  will  therefore  radiate 
heat,  which  would  result  in  the  establishment  of  some  inter- 
mediate equilibrium  temperature  below  the  true  freezing 


FREEZING  POINTS  AND  BOILING  POINTS 


279 


point  of  the  liquid  under  investigation.  Then,  too,  the 
rate  of  stirring  will  affect  the  equilibrium  temperature  as 
well  as  the  amount  of  ice  which  separates  at  the  time  of 
freezing  the  solution.  Hence  it  is 
evident  that  unless  this  equilibrium 
temperature  does  not  coincide  with 
the  freezing  point,  the  reading  of  the 
thermometer  will  not  record  the  true 
freezing  point  of  the  liquid. 

Recent  investigators  have  aimed 
to  produce  conditions  such  as  to 
eliminate  as  many  of  these  sources 
of  error  as  possible,  with  the  result 
that  the  values  of  Kp  for  a  large 
number  of  solvents  are  fairly  accu- 
rately known.  For  water  the  ac- 
cepted value  of  Kp  is  18.6.  That " 
is,  one  mole  of  the  solute  when  dis- 
solved in  100  grams  of  the  solvent 
will  lower  the  freezing  point  of 
water  18.6°;  if  one  mole  is  dis- 
solved in  one  liter  (1000  grams)  the 
constant  becomes  1.86,  i.e.  the  freezing  point  is  lowered 
1.86°.  If  one  mole  could  be  dissolved  in  one  gram  of 
solvent,  the  freezing  point  would  be  lowered  1860°,  i.e.  the 
freezing  point  constant  is  1860.  Various  authors  use  these 
different  values  for  KF,  and  hence  more  or  less  confusion  may 
arise.  In  Table  XLVI  we  saw  that  in  one  of  the  columns 
are  given  abnormal  values  for  the  molecular  lowering  of  the 
freezing  point ;  an  explanation  of  these  will  be  taken  up  sub- 
sequently. 

Boiling  Point  Method.  —  By  referring  to  Fig.  83  it  will  be 
observed  that  if  pz  represents  the  vapor  pressure  of  the  pure 
solvent  and  is  one  atmosphere,  then  the  boiling  point  is  ts, 
and  for  a  solution  of  such  concentration  that  its  vapor  pres- 


FlG.    84. 


280 


PHYSICAL  CHEMISTRY 


sure  curve  is  represented  by  CE,  the  boiling  point  would  be 
represented  by  24.     The  boiling  point  of  the  solvent  has  been 

raised  by  the  addi- 
tion of  the  solute 
from  /3  to  /4,  that 
is,  the  rise  of  the 
boiling  point  is  /4  — 
/3,  while  the  pres- 
sure has  remained 
constant. 

That  the  rise  of 
the  boiling  point 
of  solutions  is  pro- 
portional to  the 
concentration  was 
emphasized  by 
Raoult  and  has 
been  confirmed  sub- 
sequently. Raoult 
devised  a  method 
by  means  of  which 
these  small  changes 
can  be  measured 
accurately;  in  Fig. 
85  is  represented 
the  general  form  of 
the  apparatus.  As 
in  the  freezing  point 
method  sointheboil- 
ing  point  method  a 
constant  quantity 
of  the  solvent  is 


FIG.  85. 


employed,  S,  in  which  g  grams  of  the  solute  are  dissolved, 
and  a  rise  of  the  boiling  point  of  A  degrees  is  obtained.  A 
formula  similar  to  that  obtained  by  the  freezing  point  method 


FREEZING  POINTS  AND   BOILING  POINTS  281 

may  be  obtained,  from  which  the  molecular  weight  of  the 
solute  may  be  calculated,  that  is,  m  =  -^^ — ^,  in  which  KB 

is  the  molecular  rise  when  one  mole  of  the  solute  is  dissolved 
in  100  grams  of  the  solvent. 

An  additional  discussion  of  these  two  methods  and  the 
significance  of  the  constants  will  be  presented  in  the  following 
chapter. 


CHAPTER  XXVI 
THERMODYNAMIC   CONSIDERATIONS 

ABOUT  1798  Count  Rumford's  experiments  on  the  boring 
of  cannon  convinced  him  that  heat  is  nothing  more  than 
energy  of  motion.  Heat  had  been  termed  caloric,  an  igneous 
fluid,  and  this  new  view  received  but  slight  attention  until 
the  determination  of  a  numerical  relation  between  the  quan- 
tity of  work  and  quantity  of  heat  made  by  Robert  Mayer 
(1842)  and  by  James  Prescott  Joule  (1843)  were  published. 
Various  experiments  in  this  field  have  been  performed,  such 
as  the  heat  effects  produced  by  the  friction  of  liquids,  by  the 
compression  of  gases,  heating  effect  of  electric  currents ;  and 
the  agreement  between  the  results  is  as  close  as  the  errors  of 
experimentation  justify.  These  lead  to  the  formulation  of 
the  Principle  of  Equivalence,  familiarly  known  as  the  First 
Law  of  Thermodynamics  or  the  Mayer- Joule  Principle : 

11  When  heat  is  transformed  into  work,  or  conversely  when 
work  is  transformed  into  heat,  the  quantity  of  heat  gained  or 
lost  is  proportional  to  the  quantity  of  work  lost  or  gained." 

The  old  fundamental  notion  that  a  body  or  system  "  con- 
tains so  much  heat  "  necessitates  obtaining  a  clear  conception 
of  the  terms  heat,  work,  and  energy. 

If  we  have  a  given  mass  of  a  gas  under  specified  conditions 
of  pressure  and  temperature,  it  will  occupy  a  certain  volume. 
If  this  gas  be  brought  into  contact  with  a  body  at  a  higher 
temperature  and  the  pressure  remain  constant,  the  volume 
will  increase,  which,  under  suitable  conditions,  would  result 
in  doing  mechanical  work.  The  system  receives  heat  energy 
from  an  external  source  and  in  turn  does  mechanical  work. 
The  relation  between  the  heat  energy  imparted  and  the 

282 


THERMODYNAMIC   CONSIDERATIONS  283 

mechanical  energy  obtained  is  represented  in  the  statement 
that  the  total  energy  gained  by  a  body  is  equal  to  the  energy 
supplied  to  it  in  the  form  of  heat,  and  in  any  other  form  of 
energy,  i.e.  the  energy  supplied  in  the  form  of  heat  can  be 
obtained  in  the  form  of  work,  and  energy  supplied  as  work  is 
withdrawn  as  heat.  These  are  statements  of  the  law  of  Con- 
servation of  Energy. 

It  is  only  under  perfect  conditions  that  one  form  of  energy 
can  be  completely  transformed  into  another,  and  the  reverse 
transformation  accomplished.  Such  a  process  is  termed 
reversible.  All  processes  are  actually  irreversible.  The 
maximum  quantity  of  heat  that  can  be  converted  into  work 
by  any  machine  depends  upon  the  Principle  of  Carnot- 
Clausius  and  is  known  as  the  Second  Law  of  Thermo- 
dynamics or  the  Law  of  Degradation  of  Energy.  "Heat 
cannot  pass  from  a  colder  to  a  warmer  body  without  some 
compensating  transformation  taking  place,"  or  "  //  is  impos- 
sible by  means  of  a  self-acting  machine  unaided  by  any  ex- 
ternal agency  to  convey  heat  from  one  body  to  another  at  higher 
temperature,"  or  "No  change  in  a  system  of  bodies  that  can 
take  place  of  itself  can  increase  the  available  energy  of  the 
system." 

Availability  of  Energy.  —  Mechanical  energy  as  well  as 
electrical  energy  can  be  completely  transformed  into  heat 
energy,  but  heat  energy  cannot  be  completely  converted 
into  mechanical  energy. 

It  is  not  the  actual  amount  of  energy  a  system  possesses, 
but  the  amount  that  can  be  utilized  in  any  special  trans- 
formation desired,  that  is  of  importance;  that  is,  it  is  the 
part  of  the  energy  present  that  is  available  and  that  can  be 
utilized  in  any  particular  transformation. 

Let  dU  represent  the  increase  of  the  intrinsic  energy  of  a 
system  when  the  work,  dW,  is  done  by  the  addition  of  the 
quantity  of  heat,  dQ.  Then, 

dQ  =  dU  +  dW. 


284  PHYSICAL   CHEMISTRY 

This  is  the  quantity  of  heat  absorbed  by  the  system,  which 
increases  its  intrinsic  energy  and  does  external  work.  In 
this  equation  Q,  U,  and  W  are  measured  in  the  same  units 
of  energy.  If  Q  is  measured  in  heat  units  and  U  and  W  in 
mechanical  units,  Joule's  equivalent,  /,  must  be  used  on 
the  left-hand  side.  We  consider  dQ  positive  when  the  sys- 
tem absorbs  heat,  negative  when  it  gives  out  heat ;  dW  is 
positive  when  work  is  done  by  the  system,  dU  is  positive 
when  the  intrinsic  energy  is  increased  during  the  trans- 
formation. 

Carnot's  Cycle.  —  Since  it  is  impossible  to  obtain  work 
from  the  heat  of  a  system  unless  there  is  another  system  at 
a  lower  temperature,  Carnot  showed  that  it  is  possible  to 
obtain  work  continuously  from  the  two  systems  at  different 
temperatures  by  employing  a  third  intermediate  system  and 
causing  it  to  undergo  a  series  of  cyclic  transformations 
known  as  Carnot's  Cycle. 

Suppose  we  have  two  systems,  5,  a  source,  and  R,  a  re- 
frigerator, at  the  constant  temperatures  /i  and  /2,  respec- 
tively, with  /i  >  /2.  If  they  are  placed  in  contact,  heat  will 
flow  from  5  to  R  and  no  work  will  be  done ;  but  if  they  are 
kept  separated  and  a  third  system,  M,  used  to  convey  the 
energy,  work  can  be  obtained. 

1.  The  system  M  at  the  temperature  h  is  brought  by  some 
convenient  mechanical  means,  without  gain  or  loss  of  heat, 
to  the  temperature  /i  (for  a  gaseous  system,  by  compres- 
sion).    This  is  called  adiabatic  action. 

2.  It  is  now  placed  in  contact  with  the  system  5  and  re- 
ceives from  it  a  certain  quantity  of  heat,  Qi,  while  its  tem- 
perature remains  constant  and   equal  to  t\.     The  system 
M  also  expands  and  does  work.     This  is  called  isothermal 
action,  as  there  is  no  change  of  temperature. 

3.  The  temperature  is  now  allowed  to  fall  to  h  without 
the  medium  receiving  or  parting  with  heat  (by  expansion  of 
a  gas).     Adiabatic  action. 


:/**ftW 


Voknw 


THERMODYNAMIC  CONSIDERATIONS  285 

4.  The  system  M  is  brought  in  contact  with  the  refrig- 
erator R  and  is  allowed  to  return  to  the  initial  state.  During 
this  change  a  certain  quantity  of  heat,  Q2,  is  given  up  to  the 
refrigerator.  Isothermal  action.  0 

This  may  be  represented  diagrammatically  by  the  p-V 
diagram,  Fig.  86. 

1.  At  the  volume  and  pressure  designated  by  A  at  the 
temperature  /2,  by  adiabatic  compression  the  volume  will 
change  as  indicated  by  the  line  AB  without 

gain  or  loss  of  heat. 

2.  Along   the   isothermal   line   BC  we 
have    the    change    of  volume    indicated, 
while  the  quantity  of  heat,  Qi,  is  being 
absorbed  by  the  system  at  the  constant  FlG  86 
temperature  t\. 

3.  During  the  fall  in  temperature  the  adiabatic  line  CD 
represents  the  change  in  volume  through  expansion  while 
cooling  to  the  temperature  ^. 

4.  The  isothermal  DA  at  temperature  k  represents  the 
change  during  which  the  quantity  of  heat  Q2  has  been  given 
up  to  the  refrigerator. 

This  is  known  as  the  Carnot  Cycle,  and  the  work  done  in 
the  cycle  is  represented  by  the  area  A  BCD.  The  differ- 
ence Qi  —  02  is  the  heat  transformed  into  work.  This 
process  could  be  reversed.  Then  we  should  have  the  same 
area,  A  BCD. 

By  this  perfectly  reversible  process,  the  Carnot  Cycle,  work 
can  be  derived  indefinitely  from  a  single  source  and  re- 
frigerator maintained  at  given  constant  temperatures,  but 
since  this  cannot  be  exactly  obtained  on  account  of  resist- 
ance, friction,  velocity,  etc.,  the  resulting  cycle  in  practice 
is  irreversible,  and  consequently  the  maximum  work  cannot 
be  obtained. 

Efficiency  is  defined  as  the  ratio  between  what  is  obtained 
to  that  which  might  be  obtained.  The  quantity  of  heat  Q\ 


286  PHYSICAL   CHEMISTRY 

is  the  amount  that  is  supplied,  but  Qi  —  Q2  is  the  amount 
that  is  transformed,  or  it  is  the  part  of  Q\  that  is  actually 

available ;  then  the  ratio  ^l  ~  ^2  is  called  the  efficiency,  or 

the  availability  of  Q\  for  transformation  into  work. 

If  reversible  cycles  are  operated  between  the  same  source 
and  refrigerator,  they  have  the  same  efficiency.  This  is 
seen  as  follows  :  Let 


If  the  more  efficient  cycle  be  used  as  an  engine  moving 
directly  to  drive  the  less  efficient  cycle  in  a  reverse  direction, 
the  numerators  which  represent  the  work  would  be  equal, 
and  hence  Qu>  >  Q\a.  This  means  that  the  cycle  b  returns 
more  heat  to  the  source  than  cycle  a  takes  from  the  source  ; 
or,  heat  flows  from  a  point  of  low  temperature  to  a  point  of 
high  temperature.  This  is  impossible,  and  hence  cycle  a 
cannot  be  more  efficient  than  b.  In  the  same  way  b  cannot 
be  more  efficient  than  a.  The  efficiencies,  therefore,  are 
equal.  If  a  were  a  non-reversible  cycle,  the  above  proof 
would  show  that  it  could  not  have  a  higher  efficiency  than 
that  of  6,  but  we  could  not  prove  that  it  was  less.  In  other 
words,  no  cycle  can  be  more  efficient  than  a  reversible  cycle 
when  acting  between  the  same  source  and  refrigerator. 
The  reversible  cycle  therefore  has  the  maximum  efficiency. 

The  absolute  temperature  is  sometimes  defined  by  the 
statement  that  the  absolute  temperatures  of  two  bodies  are 
proportional  to  the  quantities  of  heat  given  up  by  one  body 
to  the  medium  and  rejected  by  the  medium  to  the  other  in 
the  Carnot  cyclic  transformation  in  which  the  bodies  play 
the  part  of  source  and  refrigerator.  Using  this  concept, 
we  have 

T,-  Tz 


Or      TV 


THERMODYNAMIC   CONSIDERATIONS 


287 


would  be  the  value  of  the  efficiency  of  the  Carnot  Cycle. 
The  portion  of  the  heat  energy  available  for  work  between 

the  two  temperature  limits,  TI  and  T2,  would  be      1  ~ — - 


s 


which  is  designated  the  availability.     So  if  Qi  is  the  quantity 
of  heat  absorbed  by  a  system  at  the  temperature  7\,  then 

(1/7-        T  \ 
— ^F ") 
1 1       / 

the  quantity  available  for  useful  work,  and  [  — )  Q\  is  the 

\TJ 

quantity  unavailable,  or  the  waste ;  or  the  Available  Work  = 

Oi'fr- 

Applications  to  Solutions.  —  The  following  is  van't  HofPs 
proof  of  the  application  of  The  Gas  Law  to  dilute  solutions, 
and  is  virtually  his  own  presentation :  By  means  of  a 
reversible  cyclic  process  carried  out  at  a  constant  tempera- 
ture, T,  one  mole  of  the  dissolved  sub-  i 
stance  is  to  be  removed  from  an  aqueous 
solution  in  the  form  of  a  gas  and  restored 
to  it  again.  By  raising  the  pistons  A  and 
B,  Fig.  87,  remove  the  solute  through  oc, 
a  semipermeable  membrane  impervious 
to  the  solvent.  Remove  the  pure  solvent 
to  the  outside  through  the  walls  ab  and 
cd,  which  are  impervious  to  the  dissolved 
substance,  so  as  to  maintain  a  con- 
stant concentration.  By  the  two  pistons,  A  and  B,  the 
equilibrium  is  to  be  maintained  between  the  gas  pressure 
and  the  osmotic  pressure.  At  the  temperature  TI  and 
pressure  pi  one  mole  of  the  solute  will  occupy  a  volume  V\ 
as  a  gas.  The  absorption  of  the  gaseous  solute  is  such  that 
the  gas  is  in  equilibrium  with  a  solution  that  contains  one 
mole  of  the  solute  in  volume  VQ,  the  osmotic  pressure  of 
which  is'-p^. 


Gas 


Soiu&an 


Solvent 


FIG.  87. 


288  PHYSICAL   CHEMISTRY 

The  action  desired  includes  the  following  steps  : 

I.  If  both  pistons  be  moved  upward,  one  mole  of  the 
soltite  may  be  removed  reversibly  and  at  constant  pressure 
from  the  solution,  and  the  amount  of  work  done  by  it  on  A 
is  piVi.     By  The  Gas  Law 

piV,.  =  RT,  (i) 

An  amount  of  work  is  performed  by  B  against  the  constant 
osmotic  pressure,  which  will  be  expressed  with  a  negative 

signas     '-.:'     -    -POVO         \  w 

II.  By  a  second  process  restore  the  solute  to  the  solution. 
First  let  the  gas  expand  isothermally  to  an  infinite  volume, 
Foo,  and  in  so  doing  perform  work 


This  infinitely  diluted  gas  may  now  be  brought  into  con- 
tact with  the  volume  VQ  of  solvent,  and  under  these  cir- 
cumstances the  solvent  would  not  absorb  any  of  the  gas 
because  the  gas  pressure  is  zero. 

III.  Now  let  the  piston  be  lowered  so  that  the  solute  is 
brought  into  solution,  as  the  pressure  rises.  The  expenditure 
of  work  is  rv 

-J    "pdV. 

Jo 

Here,  however,  p  has  not  the  value  given  by  pV  =  RT, 
but  a  smaller  value,  because  a  part  of  the  vapor  has  gone 
into  solution,  as  the  pressure  rises.  This  part  is  exactly  one 
mole  when  the  pressure  has  increased  to  pi,  and  consequently 
if  Henry's  Law  be  true,  when  the  pressure  is  p,  the  quantity 
of  gas  absorbed  amounts  to  p/pi  moles  :  the  undissolved  part 
remaining  is  therefore  (i  —  p/pi)  moles  and  p  may  be  cal- 
culated from 

pV=(i  -p/pj  RTi  =  RTl-pVl 


THERMODYNAMIC   CONSIDERATIONS  289 

so  that  RTi 

"  Y  +  Vi' 

Consequently  the  work  done  is 


since  V^  is  infinitely  great,  in  comparison  to  FI,  the  expres- 
sion becomes  T/ 

-RTtlog.**.  (4) 

Since  the  total  work  done  in  a  reversible  cyclic  process 
at  constant  temperature  must  be  zero  because  the  cycle  of 
Fig.  83  would  have  no  area, 

(i)  +  (2)  +  (3)  +  (4)  =  o 
and 


or  p0V0  = 

But  piVi  = 

since  T\  is  constant  we  see  that  for  equal  values  of  V\  and 

VQ  we  must  have  p  =  p 

From  this  we  see  that  for  any  dissolved  body  which  con- 
forms to  Henry's  Law,  for  the  same  temperature  and  con- 
centration the  gas  pressure  and  the  osmotic  pressure  of  its 
solution  must  be  equal. 

Assuming  that  a  gas  dissolving  according  to  Henry's  Law 
has  the  same  molecular  character  in  the  solution  and  in  the 
gas,  we  may  consequently  draw  all  the  conclusions  as  to 
the  osmotic  pressure  of  dissolved  bodies  that  have  been 
drawn  as  to  gas  pressure  or  vapor  pressure,  i.e.  we  may 
apply  Avogadro's  Law  to  solutions,  making  use  of  the 
osmotic  pressure  instead  of  the  gas  pressure.  It  follows 
that  The  Gas  Law  can  be  applied  to  solutions. 


2QO  PHYSICAL   CHEMISTRY 

Relation  between  Lowering  of  Vapor  Pressure  due  to  the 
Solute  and  the  Osmotic  Pressure 

By  making  use  of  the  fundamental  conceptions  of  thermo- 
dynamics van't  Hoff  showed  by  the  following  isothermal 
reversible  cyclic  process  the  relation  between  the  osmotic 
pressure  and  the  lowering  of  the  vapor  pressure  of  the  solvent 
due  to  the  presence  of  a  non-  volatile  solute. 

Let  us  assume  that  we  have  a  solution  containing  a  non- 
volatile solute,  the  vapor  pressure  of  the  solution  being  pi 
and  that  of  the  solvent  p.  Then,  as  shown  above,  p  >  pi. 
Let  po  be  the  osmotic  pressure  of  the  solution. 

The  following  order  in  the  cyclic  process  is  taken  : 

I.  By  means  of  a  semipermeable  membrane  as  a  piston, 
remove  through  the  piston  osmotically  and  reversibly  the 
amount  of  the  solvent  containing  one  gram-molecule  of  the 

,-,  £•« 

solute,    i.e.  ^—  grams.     Then  VQ  =  -  •     The  work  done 

g  gP 

is  P0V0  where  V0  is  the  volume  in  which  one  mole  of  the 

solute  is  dissolved  and  p0  the  osmotic  pressure. 

II.  Now  restore  reversibly  this  quantity  of  solvent  by 
distilling  it,   expanding  iso  thermally  to   pressure  pi,   con- 
densing, and  returning  this  solvent  to  the  solution. 

At  the  temperature  T  and  pressure  p  we  gain  a  quantity 
of  work  done  by  the  reversible  evaporation. 

By  expanding  this  vapor  (which  is  considered  to  be  a  gas) 
at  the  temperature  T  to  the  pressure  pi,  an  additional 
quantity  of  work  is  gained.  For  one  mole  of  the  vapor  of 
the  solvent  the  work  gained  would  be 


pi 

and  for  the  mass  containing  one  gram-molecule  of  the  solute, 
it  would  be  ySRT^t_, 

gM  pi 


THERMODYNAMIC  CONSIDERATIONS  291 

Finally,  the  vapor  is  to  be  condensed  in  contact  with  the 
solution  at  pi  and  T,  in  which  process  the  work  gained  by 
evaporation  is  used  up.  The  heats  required  for  evapora- 
tion and  obtained  from  condensation  are  assumed  equal. 
Since  this  cyclic  process  has  been  carried  out  at  constant 
temperature,  the  net  work  is  zero  as  before,  and  the  osmotic 
work  spent  must  equal  the  work  of  expansion  gained, 


Substituting  for  VQ  its  value  above,  we  obtain 
.   mS      mS  r>-ri        P 

Pn  -  =  TT  •*- 

F°  gp        Mg 

from  which  we  get 


Pi      PRT 

which  is  the  relation  sought.     In  dilute  solutions  p0V0  = 
nRT  where  n  =  number  of  molecules  dissolved  in  volume 

Vo.    From  this,  since  JL2-  =  -—  ,  substituting  we  have 

RT    y.o 

\OZP  =  Mn_. 
S>i       P  Vo 

This  is  an  accurate  form  of  Raoult's  Law.     If  the  differ- 
ence between  p  and  pi  is  small  one  may  substitute  in  place 

1  and  obtain 
p 

p  —  pi  _  M  PQ 
p        ~~  p  RT 
i  _  M  n 


P  Vo 

Since  —  =  V"(moie),  the  volume  of  one  mole  of  the  solvent 
P 

and  V0  is  the  volume  of  the  solution  which  when  very  dilute 


292  PHYSICAL   CHEMISTRY 

becomes  the  volume  of  the  solvent,  hence  Vo/  ^(moie)  =  A/", 
the  number  of  moles  of  the  solvent.  This  is  the  reciprocal 
of  what  we  have  in  the  formula,  hence  we  have 

p       =~N* 
This  is  the  form  of  Raoult's  Law  previously  used. 

Relation  between  the  Osmotic  Pressure  and  the  Lowering  of 
the  Freezing  Point  of  the  Solvent  due  to  a  Non-volatile 
Solute 

The  following  cyclic  process  showing  the  relationship  be- 
tween the  osmotic  pressure  of  solutions  and  the  lowering 
of  the  freezing  point  of  the  pure  solvent  when  the  non- 
volatile solute  is  present  cannot  be  carried  out  at  constant 
temperature  and  hence  involves  the  Second  Law  of  Thermo- 
dynamics. 

Let  us  assume  that  we  have  a  large  mass  of  a  very  dilute 
solution  such  that  when  the  amount  of  the  solvent  that 
contains  one  mole  of  the  solute  is  removed  the  concentra- 
tion of  the  solution  remains  practically  constant.  Since 
the  solution  is  very  dilute,  the  change  in  the  freezing  point 
is  very  small ;  and  when  the  volume  of  solvent  containing 
one  mole  has  been  removed,  the  volume  change  is  very  small. 

Let  us  suppose  that  we  have  this  solution  so  inclosed  that 
by  means  of  a  frictionless  semipermeable  piston  we  can  re- 
move the  desired  quantity  of  solvent,  at  the  temperature 
of  the  freezing  point,  T,  of  the  pure  solvent.  Allow  this  to 
freeze;  cool  the  whole  system  to  the  freezing  point  of  the 
solution  T  —  A/.  Bring  the  ice  in  contact  with  the  solu- 
tion and  allow  it  to  melt  and  become  part  of  the  solution. 
Finally  warm  the  whole  system  up  to  its  original  tempera- 
ture, then  we  shall  be  back  to  the  initial  state,  having  com- 
pleted the  cyclic  transformation.  We  have  the  following 
stages  in  this  reversible  process : 


THERMODYNAMIC   CONSIDERATIONS  293 

I.  At  the  temperature  of  the  freezing  point,  7",  of  the  pure 
solvent  we  have  done  work  in  removing  osmotically  by 
means  of  the  semipermeable  piston  the  quantity  of  the 
solvent  containing  one  mole  of  the  solute.     There  have 

been  removed  — —  grams  of  the  solvent  at  this  temperature. 

g 

The  external  work  done  against  the  osmotic  pressure  po 
is  POVQ  mechanical  units  or  ApQV0  calories,  where  VQ  is  the 
volume  of  solvent  removed  and  A  is  the  conversion  factor. 

II.  Now  allow  these  -  -  grams  of  the  solvent  to  freeze 

isothermally  and  in  doing  so  there  will  be  liberated  LF  — ^ 

g 

calories  of  heat  at  the  temperature  T,  where  LF  is  the  latent 
heat  of  fusion  of  one  gram  of  the  solid  solvent. 

III.  Now  cool  adiabatically  the  solution  and  also  the  - 

grams  of  the  solvent  which  is  now  ice,  to  the  temperature 
T  -  AT. 

IV.  At  this  lower  temperature  (T  —  AT")  we  place   the 
ice  in  contact  with  the  solution,  allow  it  to  melt  and  to  be- 
come a  part  of  the  solution  again.     In  melting,  the   heat 

absorbed  at  this  lower  temperature  is  Lrr  — —  calories. 

g 

V.  Now  raise  the  temperature  of  the  whole  system  adia- 
batically to  the  original  temperature   T,  during  which  no 
heat  is  given  out  or  absorbed. 

This  is  a  reversible  cyclic  process,  and  the  sum  of  the 
work  terms  is  zero.  The  work  in  III  is  equal  and  opposite 
in  direction  to  that  in  V,  and  therefore  they  may  be  neg- 
lected. We  shall  then  have 

T/         T    Sm  ,     j  ,Sm 
Povo~  L*—  +  L*  —  =° 

8  8 

or  ^  y    =  £  —  -L  '  — 

POV  o       ^'  „        ^f     „  - 


2Q4  PHYSICAL   CHEMISTRY 

r- 

But  Lf  —  is  the  heat  absorbed  by  the  system  at  the  higher 

g 
temperature,    TI.     Let  us  designate  this  by  Q\  and  the 

heat,   LF'—,  given  up  at  the  lower  temperature,  we  will 

8 
designate  by  Qz.     On  substitution  we  have 

P0V0  =  Qx  -  ft. 

But  from  the  equation  ^1  ~  ^  =      l  ~  —  ?,page  286,  we 

Qi  f  i 

should  have  on  substitution,  since  TI  —  T2  =  AT 


.    T7         T   SmAT 
or  p0V0  =  LF—~—. 

We  assumed  that  The  Gas  Law  for  ideal  gases  holds  in 
the  case  of  infinitely  dilute  solutions.  Hence  for  the  osmotic 
pressure  at  the  freezing  point  T\  of  the  pure  solvent  we  will 
have  upon  the  basis  of  this  assumption  p0V0  =  RT\.  Sub- 
stituting in  the  above  the  value  of  P0V0,  we  have^ 

D  T        Lp  Sm  A  T 
rC/i«  --  —• 

g       TI 

Solving  for  the  slight  temperature  difference  AT  which 
we  will  designate  as  A,  we  have 


LfSm 
which  gives  us 

mA 


g      '  LPS 

the  gram-molecular  lowering,  since  it  is  the  lowering  of  the 
freezing  point  of  a  solution  of  one  mole  of  the  solute  con- 
tained in  5  grams  of  the  solvent.  It  is  customary  to  take 


THERMODYNAMIC  CONSIDERATIONS  295 

ioo  grams  of  the  solvent,  then  5  =  100,  which  on  substitu- 
tion gives 

mA 


g         ioo  L 

We  have  previously  seen  (page  26)  that  the  gas  constant, 
R,  is  equal  to  84,780  gram-centimeters  per  degree. 

i  calorie  is  4.186  Joules,  and  i  Joule  is  -^-  gram-centimeters. 

981 

i  calorie  =  —  -  X  I0   or  42,670  gram-centimeters. 
981 

Then    ^  °  =  1.987  calories  per  degree  as  the  value  of  R, 
42670 

or  R  =  2  calories  per  degree  approximately. 
Substituting,  the  equation  takes  the  form 

2  T2  ,. 


g        ioo  L 

as  the  expression  for  the  gram-molecular  lowering  of  the 
freezing  point  when  T  is  the  freezing  point  of  the  pure  solvent 
expressed  on  the  absolute  scale. 


The  left-hand  member     —  is  the  form  of  the  expression 

g 
used  by  Raoult,  which  he  stated  was  equal  to  a  constant 

Kf.     ^—  =  K,  is  the  empirical  formula  obtained  by  him  and 

g 

subsequently  confirmed  by  numerous  experimenters.  It 
states  that  the  lowering  of  the  freezing  point,  when  one 
mole  of  various  solutes  is  dissolved  in  the  same  arbitrarily 
selected  quantity  (ioo  grams)  of  a  solvent,  is  a  constant 
quantity.  Hence  it  is  evident  that  the  right-hand  member 
of  equation  (i)  must  also  represent  this  same  constant. 
Therefore,  knowing  T,  which  is  the  temperature  of  the  freez- 
ing point  of  the  pure  solvent,  and  Lp,  which  is  the  latent 

heat  of  fusion  of  the  pure  solvent,  the  value  of   2         can  be 

IOO  L 


296 


PHYSICAL  CHEMISTRY 


readily  ascertained,  which  is  the  value  of  the  gram-molecu- 
lar lowering  of  the  solvent.  There  is  no  term  in  this  ex- 
pression which  relates  to  the  dissolved  substance,  hence  the 
character  of  the  solute  should  not  affect  the  value,  and  we 
are  justified  in  drawing  the  conclusion  that  the  gram-mo- 
lecular lowering  of  the  freezing  point  is  a  constant  and  inde- 
pendent of  the  solute,  i.e.  — — — -  =  KP  =  ^—  =  gram- 

100  LF  g 

molecular  lowering. 

We  have  then  two  experimental  methods  by  means  of 
which  the  value  of  this  constant,  KF,  can  be  determined : 
(i)  as  Raoult  did,  by  determining  the  lowering  produced 
by  the  freezing  point  method,  (2)  as  van't  Hoff  did,  by  cal- 
culating the  value  of  KF  from  the  latent  heat  of  fusion  of 
the  solvent.  The  agreement  between  the  two  methods  is 
very  close,  as  the  values  in  Table  XLVII  show,  wherein 
the  quantity  of  the  solvent,  5,  employed  is  100  grams. 


TABLE  XLVII 


SUBSTANCE  AS  SOL- 
VENT 

FREEZING 
POINT 

LATENT  HEAT  OP 
FUSION,  CALORIES 
PER  GRAM 

FREEZING  POINT  CONSTANT 

Determined  Ex- 
perimentally 

Kf-*T 

Calculated  from 
van't  Hoff  's 
Formula 
K-            RT* 

looLp 

Water 
Acetic  acid 
Benzene 
Naphthalene 
Nitrobenzene 
Phenol  .     . 
Thymol      . 
Benzophenone 

0° 
17  ' 
5-5 
80.  i 
6.0 
38 
48.2 
48.1 

79-7 
43-7 
304 
35-6 
22.5 
24.9 
27-5 
23-7 

18.6 

39 
51-2 
69 
70 

74 
80 
98 

18.58 
38.2 
50.7 
69-5 
68.4 
78 

74-5 
86.4 

The  value  for  the  latent  heat  of  fusion,  LF,  for  nitrobenzene 
had  not  been  determined,  and  van't  Hoff  calculated  it  from 
the  value  of  KF,  obtained  experimentally  and  found  it  to  be 


THERMODYNAMIC  CONSIDERATIONS  297 

22.1  calories  per  gram.  Pettersson  subsequently  determined 
the  latent  heat  and  found  it  to  be  22.3  calories.  Similarly 
for  ethyl  bromide,  from  the  value  of  Kp  the  latent  heat  was 
calculated  and  found  to  be  13,  and  Pettersson  's  subsequent 
determination  was  12.94.  So  it  is  evident  that  the  freezing 
point  constant  can  be  employed  to  calculate  the  latent  heat 
of  fusion  by  van't  Kofi's  formula. 

The  equation  for  the  lowering  of  the  freezing  point  then 
takes  the  form 

mA 


in  which  A  is  the  lowering  when  g  grams  of  the  solute  are 
dissolved  in  100  grams  of  the  solvent, 

or  mA  _  100  KF 

~    ~~s~ 

in  which  A  is  the  lowering  when  g  grams  of  solute  are  dis- 
solved in  5  grams  of  the  solvent. 
Solving  for  m,  we  have 


as  the  general  Freezing  Point  Equation. 

Relation  between  the  Osmotic  Pressure  and  the  Elevation 
of  the  Boiling  Point  of  the  Solvent  due  to  a  Non-volatile 
Solute 

By  evaporation  at  the  boiling  point  of  the  solution,  T  -f  A  T, 
remove  from  a  large  mass  of  a  very  dilute  solution  a  quantity 
of  the  solvent  that  would  contain  one  mole  of  the  solute 
without  materially  changing  the  concentration  of  the  solu- 
tion; cool  the  vapor  separated  and  the  solution  to  the 
temperature  of  the  boiling  point  of  the  pure  solvent,  T; 
condense  the  vapor  and  introduce  it  osmotically  into  the 


298  PHYSICAL  CHEMISTRY 

solution  again;  raise  the  temperature  of  the  solution  to 
the  boiling  point  of  the  solution.  By  such  a  cyclic  process 
similar  to  that  employed  in  the  case  of  the  lowering  of  the 
freezing  point  relationship,  we  derive  an  expression  for  the 
elevation  of  the  boiling  point  analogous  to  that  obtained  for 
the  lowering  of  the  freezing  point,  i.e. 

wA         2  T2 


g        100  Lv 

in  which  the  terms  have  the  same  significance  as  in  the  mo- 
lecular lowering  of  the  freezing  point  equation,  except  that 
T  refers  to  the  boiling  point  of  the  pure  solvent  at  atmos- 
pheric pressure  on  the  absolute  scale,  Lr  is  the  latent  heat 
of  vaporization  of  one  gram  of  the  pure  solvent  at  the  tem- 
perature T,  and  A  is  the  rise  of  the  boiling  point.  This 
gram-molecular  elevation  is  a  constant  quantity  and  we  have 


IOO 


which  can  be  calculated  from  the  boiling  point  and  latent 
heat  of  the  pure  solvent.  As  in  the  case  of  the  lowering  of 
the  freezing  point  we  may  obtain 


SA 

the  general  Boiling  Point  Equation,  in  which  A  is  the  rise 
of  the  boiling  point  when  g  grams  of  the  solute  are  dissolved 
in  S  grams  of  the  solvent. 

Similarly  the  constant  for  the  boiling  point  can  be  obtained 
by  each  of  these  two.  methods  and  the  experimental  values 
agree  well  with  those  calculated  by  the  use  of  van't  Hoff's 
formula,  as  is  seen  from  the  values  given  in  Table  XLVIII, 
wherein  the  quantity  of  the  solvent,  5,  employed  is  100 
grams. 


THERMODYNAMIC  CONSIDERATIONS 


299 


TABLE  XLVIII 


BOILING  POINT  CONSTANT 

SUBSTANCE  AS 
SOLVENT 

BOILING 
POINT 

LATENT  HEAT  OF 
VAPORIZATION 
CALORIES  PER  GRAM 

Determined 
Experi- 
mentally 

Calculated  from 
van't  Hoff's  Formula 

K           RTl 

KR=  — 
B       g 

s~iooLr 

Chloroform 
Acetonitril 
Ethyl  alcohol 

6l.2° 

81.3 

78.8 

58.45 
170.6 
205.1 

38.80 
13.00 
11.50 

38.00 
14.60 
11.98 

Ether     .... 

35-0 

90 

21.  IO 

20.9 

Acetone 

56.3 

125-3 

I7-25 

17.2 

Acetic  acid 

118 

97 

30-7 

31.2 

Benzene 

80.3 

93 

26.7 

26.7 

Nitrobenzene 

205 

79.2 

50.1 

57-3 

Aniline  .... 

184 

U3-9 

34.1 

36.4 

Pyridine 

H5 

101.4 

29-5 

29-5 

Water    .     ;     .     . 

100 

535-8 

5-2 

5-15 

Eykmann  confirmed  the  use  of  van't  Hoff's  formula  for 
calculating  the  latent  heat  of  vaporization,  as  the  following 
results  show : 


SUBSTANCE 

Z,FBY  DIRECT  MEASUREMENT 

Ly  CALCULATED  BY  VAN'T 
HOFF'S  FORMULA 

Thymol    
Diphenyl 

27-5 
28  5 

27.9 

2Q  A 

Azobenzene       .... 

29.0 

294 

Significance  of  K.  —  The  symbol  K  then  represents  the 
change  in  the  freezing  point  (K,)  or  in  the  boiling  point 
(  KB)  of  the  solvent  produced  by  one  mole  of  the  solute  dis- 
solved in  the  arbitrarily  selected  quantity  (100  grams)  of 
the  solvent.  This  value  is  dependent  only  on  the  nature 
of  the  solvent  and  is  theoretically  independent  of  the  solute. 
Hence  the  value  of  K,  is  designated  the  gram-molecular 
lowering  of  the  freezing  point  and  can  be  determined  either 
from  the  freezing  point  measurements  or  calculated  from 


300  PHYSICAL  CHEMISTRY 

the  latent  heat  of  fusion  of  the  pure  solvent.  Similarly 
the  value  of  KB  is  designated  the  gram-molecular  rise  of  the 
boiling  point  and  can  be  obtained  experimentally  from 
boiling  point  determinations  or  calculated  from  the  latent 
heat  of  vaporization  of  the  pure  solvent. 

In  Table  XLV  are  given  the  values  for  the  freezing  point 
constant  and  in  Table  XLVI  the  boiling  point  constant  of  a 
number  of  the  most  common  solvents  used  in  making  molec- 
ular weight  determinations  when  100  grams  of  solvent  are 
employed. 


CHAPTER  XXVII 
ELECTRICAL  CONDUCTANCE 

VOLTA  recognized  two  different  types  of  conductors  of  elec- 
tricity and  upon  this  basis  divided  them  into  Conductors  of 
the  First  Class  and  Conductors  of  the  Second  Class.  Con- 
ductors of  the  First  Class  include  those  substances  in  which 
the  passage  of  the  electric  current  is  not  accompanied  by  a 
simultaneous  motion  of  matter  itself.  The  metals  belong  to 
this  class  as  well  as  some  other  good  conductors,  such  as 
certain  metallic  sulphides  and  oxides.  To  the  Second  Class 
belong  those  conductors  in  which  the  passage  of  the  electric 
current  is  accompanied  by  the  corresponding  motion  of  the 
matter  composing  them.  These  comprise  solutions  that 
conduct  the  electric  current.  This  is  the  classification  that 
is  also  recognized  to-day. 

Many  theories  have  been  proposed  in  order  to  explain  the 
mechanism  by  which  the  electric  current  passes  through  a 
conductor  as  well  as  the  various  phenomena  observed. 
Among  the  first  efforts  was  Davy's  Electrochemical  Theory, 
wherein  he  assumed  that  chemical  affinity  is  essentially  elec- 
trical. That  is,  that  the  atoms  possess  electrical  charges, 
and  when  atoms  possessing  electrical  charges  of  different  sign 
come  near  one  another  there  results  a  decomposition  and  a 
recombination  depending  upon  the  relative  strength  of  the 
charges  of  the  same  sign,  the  stronger  uniting  with  the  atoms 
having  the  charge  of  opposite  sign,  thus  producing  a  new  com- 
pound. He  also  supposed  that  a  large  number  of  atoms  of 
small  charges  of  the  same  sign  might  unite  and  form  a  unit 

301 


302  PHYSICAL  CHEMISTRY 

with  a  greater  charge  than  that  of  some  single  atom.     This 
theory  of  Davy  was  not  very  generally  accepted. 

Berzelius,  from  his  work  on  the  decomposition  of  numerous 
solutions  by  means  of  an  electric  current  obtained  from  a 
Voltaic  Pile,  concluded  that  the  compounds  in  solution  were 
electrically  decomposed  into  two  parts,  a  basic  oxide  and  an 
anhydride.  Copper  sulphate,  CuSO4,  for  example,  he  consid- 
ered as  electrically  decomposed  into  the  basic  oxide,  CuO, 
and  the  anhydride,  SOs,  which  were  respectively  positively 
and  negatively  electrified.  In  order  to  explain  such  reac- 
tions Berzelius  assumed  that  each  atom  when  in  juxtaposi- 
tion with  another  atom  possesses  two  poles,  one  electroposi- 
tive and  the  other  electronegative.  When  in  contact,  one  of 
these  poles  is  much  stronger  than  the  other,  and  the  atom 
reacts  as  though  it  were  "  unipolar."  Hence,  the  chemical 
affinity  of  an  element  depends  upon  the  amount  of  the  elec- 
trical charge  of  its  atoms  —  positively  charged  atoms  react- 
ing with  negatively  charged  atoms,  and  the  electricities  of 
opposite  signs  neutralizing  each  other,  resulting  in  the  forma- 
tion of  a  compound  electrically  positive  or  electrically  nega- 
tive, depending  upon  which  is  in  excess.  This  may  result 
from  the  direct  union  of  the  elements,  and  two  such  com- 
pounds may  in  turn  combine,  forming  a  still  $iore  complex 
substance.  The  formation  of  the  so-called  double  compounds 
is  thus  explained.  SO3  is  the  union  of  negatively  charged  S 
with  three  negatively  charged  oxygen  atoms,  resulting  in  the 
formation  of  the  strongly  negative  residue  SOs.  The  union 
of  two  negatively  charged  atoms  is  accounted  for  by  assum- 
ing that  every  atom  possesses  two  charges,  positive  and  nega- 
tive, and  that  in  each  case  the  negative  charge  predominates. 
The  negative  charge  of  the  oxygen  neutralizes  the  positive 
charge  of  the  sulphur,  giving  a  negatively  charged  com- 
pound, SOs. 

This  theory  of  Berzelius,  known  as  the  Dualistic  Theory, 
met  with  general  acceptance  and  had  a  very  pronounced 


ELECTRICAL  CONDUCTANCE  303 

influence  upon  chemistry.  Particularly  in  quantitative  anal- 
ysis and  mineralogy,  in  which  lines  Berzelius  was  a  pioneer, 
has  he  left  the  imprint  of  the  Dualistic  Theory  in  the  methods 
adopted  in  writing  the  formulae  of  minerals  and  in  reporting 
the  analysis  of  substances.  The  mineralogists  employ  this  idea 
in  writing  the  formulae  of  minerals ;  for  example,  the  formula 
for  feldspar,  K2Al2Si6Oi6,  is  written  K20  •  A12O3  •  6  SiO2. 
The  chemist  reports  his  analysis,  not  as  the  percentage 
of  the  particular  element,  but  as  the  oxide ;  thus,  calcium 
is  reported  as  CaO,  phosphorus  as  P206,  sulphur  as 
SO3,  etc.  In  this  way  the  imprint  of  the  Dualistic  concep- 
tion of  Berzelius  is  very  marked  even  to-day,  although 
many  are  making  an  effort  to  get  away  from  it,  e.g.  the 
agricultural  chemists  in  their  methods  of  reporting  their 
analytical  data. 

Many  objections  to  Berzelius'  Dualistic  Theory  arose,  and 
among  them  were  two  which  he  could  not  explain.  At  that 
time  all  acids  were  supposed  to  contain  oxygen,  but  with  the 
discovery  of  the  halogen  acids  and  their  salts  there  was 
presented  a  large  group  of  compounds  that  could  not  be  con- 
ceived as  being  composed  of  a  basic  oxide  and  an  anhydride, 
and  consequently  presented  a  most  serious  obstacle  to  the 
general  application  of  the  theory.  Liebig  called  attention, 
to  the  replacement  in  organic  compounds  of  the  positively 
charged  H  by  the  negatively  charged  Cl,  such  as  the  forma- 
tion of  the  chloracetic  acids,  CH2C1COOH,  CC13COOH  from 
CH3COOH.  These  acids  all  have  properties  similar  to  those 
of  acetic  acid. 

Recently  J.  J.  Thomson  has  shown  that  when  hydrogen 
gas  is  electrolyzed,  positive  H  appears  at  one  pole  and  nega- 
tive H  at  the  other,  from  which  he  concluded  that  the  hydro- 
gen molecule  is  probably  made  up  of  a  positive  and  a  nega- 
tive part  molecule  and  that  hydrogen  is  not  always  positive. 
He  called  attention  to  the  fact  that  we  have  negative  chlorine 
replaced  by  positive  hydrogen  without  altering  the  type 


304  PHYSICAL   CHEMISTRY 

of  the  compound.  For  example;  from  CH4  we  may  obtain 
CH3C1,  CH2C12,  CHC13,  and  CC14.  From  CHC13  vapor,  as 
well  as  from  a  study  of  the  spectra  of  the  vapor  of  methyl- 
ene  chloride,  ethylene  chloride,  and  even  CC14,  Thomson 
concluded  that  "  it  would  appear  that  the  chlorine  atoms, 
in  the  chlorine  derivatives  of  methane,  are  charged  with 
electricity  of  the  same  sign  as  the  hydrogen  atoms  they 
displace." 

Faraday,  after  having  convinced  himself  that  there  is  only 
one  kind  of  positive  and  one  kind  of  negative  electricity, 
showed  experimentally  that  the  chemical  or  magnetic  effects 
produced  in  any  circuit  are  proportional  to  the  amount  or 
quantity  of  electricity  passing  through  the  circuit.  By 
arranging  a  number  of  solutions  so  that  he  could  pass  the 
same  quantity  of  electricity  through  them,  he  demonstrated 
that  "  the  quantities  of  the  substances  separating  at  the  elec- 
trodes in  the  same  time  are  in  the  proportion  of  their  equivalent 
weights ,"  or  as  Helmholtz  states  it,  "  the  same  quantity  of  elec- 
tricity passing  through  an  electrolyte  either  sets  free  or  transfers 
to  other  conditions  always  the  same  number  of  valencies"  This 
is  known  as  Faraday's  Law,  and  the  constant  96,540  cou- 
lombs, onefaraday,  means  that  96,540  coulombs  of  electricity 
.will  deposit  one  gram-equivalent  of  a  metal  or  do  other 
chemical  work  equivalent  to  this. 

Faraday  (1839)  called  those  parts  which  migrate  through 
the  solution  under  the  electrical  stress  and  conduct  the 
electricity,  ions.  He  also  emphasized  the  fact  that  it  is  not 
easy  to  tell  what  the  ions  are,  as  frequently  they  are  not  the 
same  as  that  which  separates  out  on  the  electrodes.  In  the 
case  of  the  decomposition  of  solutions  of  sodium  hydroxide 
and  sodium  sulphate,  there  appear  at  the  electrodes  in  both 
cases,  hydrogen  and  oxygen;  but  the  parts  which  migrate 
through  the  solution  of  NaOH  are  undoubtedly  not  hydrogen 
and  oxygen  ions,  but  are  supposed  to  be  Na  and  OH  ions.  In 
the  case  of  Na2SO4  solution,  Daniells  said  if  the  ions  are 


ELECTRICAL  CONDUCTANCE  305 

Na  and  SC^,  the  sodium  reacts  with  the  water,  liberating 
hydrogen  at  one  electrode,  while  the  SO4  reacts  with  water 
at  the  other  electrode,  forming  sulphuric  acid  and  liberating 
oxygen.  The  ions  which  migrate  toward  the  cathode  are 
designated  cations,  and  those  which  migrate  toward  the 
anode  are  the  anions.  This  process  of  migration  occurs 
only  in  conductors  of  the  Second  Class,  and  substances 
which  yield  solutions  that  conduct  electricity  in  this  way 
Faraday  termed  electrolytes,  and  the  process  of  decom- 
posing the  substances  (electrolytes)  by  the  electric  current 
he  called  electrolysis. 

It  was,  however,  previous  to  this  time  that  Nicholson  and 
Carlisle  (1800)  decomposed  water  by  means  of  the  electric 
current,  and  many  attempts  were  made  to  explain  the  process 
by  means  of  which  this  occurred.  In  1805  Grotthus  pre- 
sented the  first  complete  theory  for  this  phenomenon  of  the 
conduction  of  a  current  through  the  solution  and  also  for 
the  decomposition  of  water.  His  theory  satisfied  the  scien- 
tific world  and  was  universally  accepted  until  recent  times. 
According  to  the  theory  one  electrode  is  positively  charged 
and  the  other  electrode  is  negatively  charged  by  the  electric 
current,  and  these  charges  are  communicated  to  the  mole- 
cules of  water,  which  become  polarized  and  oriented  so  that 
the  positive  part  of  the  molecules, 
the  hydrogen  atom,  all  face  in  one 
direction  and  the  negative  part,  the 
oxygen  atom,  in  the  opposite  direction. 
This  is  illustrated  in  Fig.  88.  The 
current  enters  the  solution  through 
the  anode,  and  the  positively  charged 
parts  of  the  molecules  are  all  in  the  direction  of  the  negative 
electrode  or  cathode,  by  which  they  are  attracted  and 
arrange  themselves  as  represented. 

If  the  charges  on  the  electrodes  (i.e.  the  Electromotive 
Force)  are  large  enough,  the  extreme  hydrogen  and  oxygen 


f>  ~  ^    c~+  -o   f>  -  "*  c>  ^i 
CE2D  CET3CZD  G 


CUD  CZD   CUD 


FIG.  88. 


306  PHYSICAL  CHEMISTRY 

atoms  nearest  the  electrodes  are  liberated  and  go  to  neutral- 
ize the  electrical  charge  on  the  electrodes  where  the  hydrogen 
and  oxygen  appear  as  gases ;  the  condition  is  represented  by 
II  in  the  figure.  This  leaves  the  other  parts  of  the  molecules 
free.  These  immediately  combine  with  the  free  parts  from 
the  adjacent  molecules,  and  this  decomposition  and  recombi- 
nation pass  on  throughout  the  liquid  between  the  electrodes. 
These  new  molecules  become  oriented  as  shown  in  III,  when 
the  process  just  described  is  repeated.  In  making  these 
transfers  of  parts  of  the  molecules  some  would  have  to  move 
over  a  considerable  distance. 

This  theory  of  Grotthus  calls  for  a  decomposition  of  the 
molecules.  To  accomplish  the  decomposition  of  the  mole- 
cules would  require  a  good  deal  of  energy.  Then  a  recom- 
bination would  take  place,  but  before  this  takes  place  some 
time  would  elapse,  during  which  the  particles  would  be  free. 
The  question  arose  as  to  what  would  inaugurate  the  second 
decomposition,  and  the  third,  and,  in  fact,  where  would  the 
energy  come  from  for  the  nth  decomposition.  The  ques- 
tion was  asked  whether  it  was  the  molecules  of  water  or  the 
molecules  of  the  dissolved  substance  that  were  decomposed 
and  conducted  the  electric  current.  This  was  a  point  of 
controversy  for  a  long  time,  opinion  was  divided,  and  such 
evasive  expressions  as  the  following  were  used :  "  water 
which  by  the  addition  of  sulphuric  acid  has  become  a  good 
conductor." 

In  order  to  electrolyze  a  solution  the  electromotive  force 
has  to  reach  a  certain  value  —  a  value  below  which  no  de- 
composition takes  place  and  the  affinity  of  the  atoms  would 
not  be  overcome.  Experimentally  it  has  been  found  that 
the  electric  current  can  be  made  to  pass  when  the  electromo- 
tive force  is  very  small.  For  example,  if  a  solution  of  silver 
nitrate  is  placed  between  two  silver  electrodes,  the  decomposi- 
tion of  the  silver  nitrate  with  the  deposition  of  silver  on  one 
electrode  and  the  dissolution  of  silver  from  the  other  can  be 


ELECTRICAL   CONDUCTANCE  307 

shown  to  take  place.  We  have  merely  the  transfer  of  silver 
from  one  electrode  to  another,  and  this  holds  for  all  differ- 
ences of  potential  however  small. 

It  was  Clausius,  about  fifty  years  later,  who  first  pointed 
out  this  contradiction,  and  he  stated  that  any  theory  which 
requires  the  decomposition  of  the  substance  must  be  aban- 
doned. Using  Faraday's  definition  of  terms,  Clausius  con- 
cluded that  the  individual  ions  are  not  bound  together,  but 
must  exist  uncombined  and  free  to  move  in  the  solution. 
Employing  the  conception  of  the  Kinetic  Theory  of  Gases, 
which  was  being  emphasized  by  the  scientific  world  at  the 
time,  Clausius  assumed  that  a  few  part  molecules  or  ions  are 
free  in  so  far  as  they  are  in  independent  motion  or  vibration, 
but  are  kept  close  together  by  their  chemical  affinity.  This 
affinity  is  overcome  by  the  rapid  vibrations,  and  the  mole- 
cules get  into  such  positions  that  it  is  more  convenient  for  one 
part  of  the  molecule  to  unite  with  the  other  part  of  another 
molecule  than  to  recombine  with  its  original  partner.  He 
imagined  a  continual  exchange  taking  place  between  the 
parts  of  the  molecules.  So  when  an  electric  current  passes, 
this  simply  guides  the  exchanges,  which  become  much  more 
frequent  under  the  electrical  stress.  If  we  consider  a  cross 
section  at  right  angles  to  the  direction  of  the  current, 
more  positive  ions  would  move  in  the  direction  of  the  cathode 
than  toward  the  anode,  and  more  negative  ions  would  move 
in  the  direction  of  the  anode.  As  a  result  there  would  be  a 
certain  number  of  positive  ions  going  in  one  direction  and 
negative  ions  in  the  opposite  direction.  This  motion  of  the 
two  parts  of  the  molecules  in  the  solution  causes  the  con- 
duction of  the  electricity.  Hence,  according  to  Clausius' 
Theory,  the  current  does  not  cause  a  decomposition  of  the 
molecules  but  guides  those  part  molecules  which  are  mo- 
mentarily free.  Clausius  in  his  conclusion  declares  "  every 
assumption  is  inadmissible  which  required  the  natural 
condition  of  a  solution  of  an  electrolyte  to  be  one  of  equilib- 


308  PHYSICAL   CHEMISTRY 

rium  in  which  every  positive  ion  is  firmly  combined  with  its 
negative  ion,  and  which,  at  the  same  time,  requires  the  action 
of  a  definite  force  in  order  to  change  this  condition  of  equilib- 
rium into  another  differing  from  it  only  in  that  some  of  the 
positive  ions  have  combined  with  other  negative  ions  than 
those  with  which  they  were  formerly  combined.  Every 
such  assumption  is  in  contradiction  to  Ohm's  Law." 

As  we  shall  see  subsequently,  this  theory  of  Clausius,  which 
was  very  generally  accepted,  is  the  basis  of  the  present 
theory  as  presented  by  Arrhenius ;  but  before  we  take  up  a 
consideration  of  this  it  is  necessary  to  present  some  of  the 
experimental  work  of  Hittorf  on  the  migration  of  ions,  and 
on  the  electrical  conductance  of  solutions  by  Kohlrausch, 
which  led  to  the  theory  of  free  ions  as  shown  by  Arrhenius 
and  by  Planck. 

Transference  Number.  —  In  the  electrolysis  of  a  solution 
equivalent  quantities  of  the  substances  appear  at  the  two 
electrodes.  If  a  solution  of  HBr  be  electrolyzed,  for  one  gram 
of  hydrogen  separating  on  the  cathode,  80  grams  of  bromine 
will  appear  at  the  anode ;  and  if  a  solution  of  HC1  be  em- 
ployed and  electrolyzed  until  one  gram  of  hydrogen  is  ob- 
tained, the  equivalent  of  chlorine,  35.5  grams,  is  liberated  at 
the  anode.  In  order  for  these  quantities  to  appear  at  the 
electrodes,  it  is  necessary  that  they  come  from  different  parts 
of  the  solution,  and  as  Faraday  said,  the  parts  of  the  elec- 
trolyte migrate  through  the  solution  and  conduct  the  current. 
A  current  of  one  faraday  flowing  through  a  solution  liberates 
one  gram-equivalent  of  hydrogen  (1.008  grams)  and  at  the 
same  time  there  is  liberated  at  the  anode  one  gram-equiva- 
lent of  some  other  substance.  Hence  both  of  these  quantities 
of  material  must  have  migrated  through  the  solution  to  their 
respective  electrodes  and  consequently  have  transported  their 
respective  shares  of  the  quantity  of  electricity  that  passed 
through  the  solution.  It  was  thought  that  equal  quantities 
of  electricity  moved  through  the  solution  in  opposite  direc- 


ELECTRICAL  CONDUCTANCE  309 

tions.  This  is  not  necessary,  for  it  is  conceivable  that  in 
order  to  cause  a  definite  quantity  of  electricity  to  pass  through 
a  given  cross  section  of  the  solution  we  could  imagine  all  of 
the  electricity  to  be  transported  by  the  ions  moving  toward 
the  anode,  or  that  it  could  be  divided  in  any  ratio  we  might 
choose.  If  the  ions  migrating  toward  their  respective  elec- 
trodes moved  at  the  same  speed,  they  would  carry  the  same 
quantities  of  the  current,  but  if  one  traveled  twice  as  fast, 
the  proportions  of  the  current  transported  by  each  would 
be  2  :  i. 

Let  us  assume  that  we  have  a  solution  of  HC1  and  that  the 
vessel,  Fig.  89,  containing  it  is  divided  into  three  compart- 
ments, A,  B,  and  C,  each  of  which  contains  10  gram-equiva- 
lents of  hydrogen  and  of  chlorine.  Let  us  electrolyze  until 
there  has  been  separated  one  gram  of  ^ 
hydrogen  and  35.5  grams  of  chlorine. 
Then  there  should  be  left  in  compart- 
ment C,  9  gram-equivalents  of  hydrogen, 
and  in  A  9  gram-equivalents  of  chlorine.  FlG  8g 

But  some  chlorine  ions  have  migrated 
over  to  A,  and  some  of  the  hydrogen  ions  have  wandered 
into  C.  The  question  arises,  how  much  of  these  have 
migrated  ?  If  we  assume  that  ^  gram-equivalent  of  hydrogen 
has  wandered  from  A  to  B  and  from  B  to  C,  then  there  has 
been  removed  from  C  %  gram-equivalent  of  hydrogen  more 
than  there  migrated  into  C,  hence  there  is  a  change  in  con- 
centration of  the  hydrogen  contents  of  C  as  well  as  of  A ,  while 
there  migrated  into  B  just  the  same  quantity  that  migrated 
out,  and  the  concentration  remains  constant.  Let  us  assume 
that  the  hydrogen  ions  move  five  times  as  fast  as  the  chlorine, 
then  f  of  the  transportation  of  the  electricity  should  be  done 
by  the  hydrogen  and  ^  by  the  chlorine.  In  this  case,  A 
should  have  lost  f  gram-equivalent  of  chlorine,  or  there  should 
remain  9^  gram-equivalents.  As  one  gram-equivalent  of 
hydrogen  was  deposited  from  C  and  f  was  transferred  from 


•it 


PHYSICAL   CHEMISTRY 


A  to  B  and  from  B  to  C,  there  must  be  remaining  in  C,  gf 
gram-equivalents.  The  loss  in  C,  the  cathode  chamber,  is  £ 
gram-equivalent,  and  the  loss  from  the  anode  chamber  A  is 
f  gram-equivalent.  The  ratio  of  these  losses, 

Cathode  chamber  loss  ^  gram-equivalent 
Anode  chamber  loss  f  gram-equivalent 

is  -J-,  or  the  ratio  of  the  rates  of  migration  of  the  anion  and  of 
the  cation,  i.e. 


Rate  of  migration  of  anion    _  i_ 
Rate  of  migration  of  cation  "~  5 


Loss  at  the  cathode 
Loss  at  the  anode 


Hittorf  carried  out  (1853-57)  a  larSe  number  of  experi- 
ments in  which  he  determined  the  ratio  of  the  losses  in  con- 
centration of  the  solution  about  the  electrodes  after  electroly- 
sis and  from  these  determined  the  ratios  of  the  rates  of  migra- 
tion of  the  ions.  He  found  that  it  was  not  necessary  to  elec- 
trolyze  until  one  gram-equivalent  had  been  separated,  but 
passed  the  current  a  sufficient  length  of  time 
to  get  a  marked  change  in  concentration  in 
the  electrode  chambers.  The  type  of  ap- 
paratus frequently  employed  is  illustrated  in 
Fig.  90.  After  electrolyzing  a  solution  of  sil- 
ver nitrate,  it  was  found  that  1.2591  grams 
of  Ag  had  been  deposited  in  the  electrolytic 
cell  and  the  same  amount  in  the  coulometer. 
A  unit  volume  of  the  solution  contained 
before  electrolysis  the  equivalent  of  17.4624 
grams  AgCl ;  and  after  electrolysis  16.7694  grams  AgCl, 
which  represents  a  loss  equal  to  0.5893  gram  of  silver. 
If  no  silver  had  come  into  the  cathode  liquid,  then  there 
should  have  been  a  loss  in  concentration  the  same  as 
the  amount  of  silver  deposited,  1.2591  grams,  but  there  was 
a  change  in  concentration  of  only  0.5893  gram,  hence 


FIG.  90. 


ELECTRICAL   CONDUCTANCE  311 

the  difference,  1.2591—0.5893,  or  0.6698  gram,  represents 
the  amount  of  silver  that  migrated  into  this  part  of  the 
solution.  If  as  much  silver  had  migrated  as  was  precipi- 
tated, all  of  the  current  would  have  been  transported  by  the 
silver,  and  its  share  in  transporting  the  current  would  have 
been  100  per  cent  or  unity,  and  the  NO3  would  not  have 
assisted.  But  only  0.6698  gram  migrated,  so  the  share  of 
the  current  that  deposited  1.2591  grams  of  silver  must  have 

been  — — 9-  =  0.532;  or  53. 2  per  cent  of  the  electricity  was 
1.2591 

transported  by  the  silver,  and  the  difference,  100  —  53.2  = 
46.8  per  cent,  was  transported  by  the  NOs.     Or,  representing 
this  on  the  basis  of  unity,  the  part  carried  by  the  silver 
is  0.532  and  that  by  the  NO3  is  0.468. 
In  general,  then,  if 

nc  =  transference  number  of  the  cation 
na  =  transference  number  of  the  anion 

then  nc  +  na  =  i.     It  was  seen  above  that 

the  change  in  concentration  at  the  cathode 
the  total  change  the  current  would  produce 

j        the  change  in  concentration  at  the  anode 
the  total  change  the  current  would  produce 

Dividing  the  second  by  the  first  we  have 

the  change  in  concentration  at  the  anode    _  n^f 
the  change  in  concentration  at  the  cathode  ~~  na 

The  transference  number  which  is  proportional  to  the 
speed  of  the  ions  through  the  solution  varies  with  the  tem- 
perature and  with  the  concentration,  as  Table  XLIX  illus- 
trates. 


312 


PHYSICAL   CHEMISTRY 


TABLE  XLIX  —  TRANSFERENCE  NUMBERS  OF  THE  CATIONS 
So-called  Best  Values  Compiled  by  Noyes  and  Falk 


TEMP. 
DEGREES 
C. 

GRAM-EQUIVALENTS  PER  LITER  OF  SOLUTION 

0.005 

O.OI 

O.O2 

O.O5 

O.I 

0.2 

0.3 

0.5 

i 

NaCl 

0° 

0.387 

0.387 

0.387 

0.386 

0.385 

18 

0.396 

0.396 

0.396 

0-395 

0-393 

0.390 

0.388 

0.382 

0.369 

30 

0.404 

0.404 

0.4O4 

0.4O4 

0.403 

96 

0.442 

0.442 

0.442 

KC1 

o 

0-493 

0493 

0493 

0493 

0.492 

0.491 

10 

0495 

0495 

0495 

0495 

18 

0.496 

0,496 

0.496 

0.496 

0495 

0.494 

30 

0.498 

0.498 

0.498 

0.498 

0.497 

0.496 

LiCl 

18 

0.332 

0.328 

0.320 

0.313 

0.304 

0.299 

NH4C1 

0 

0.489 

0.489 

18 

0.492 

0'492 

0.492 

30 

0.495 

0495 

NaBr 

18 

0-395 

0.395 

0-395 

KBr 

18 

0495 

0495 

AgN03 

18 

0.471 

0.471 

0.471 

0.471 

25 

0.477 

0.477 

0.477 

30 

0.481 

0.481 

0.481 

0.481 

0.481 

0.48l 

0.48l 

0.481 

HC1 

o 

0.847 

0.846 

0.844 

0.839 

0-834 

18 

0.832 

0.833 

0.833 

0.834 

0.835 

0.837 

0.838 

0.840 

0.844 

30 

0.822 

0.822 

0.822 

96 

0.748 

HNO3 

20 

0.839 

0.840 

0.841 

0.844 

BaCl2 

0 

0-439 

0.437 

0.432 

16 

0.420 

0.408 

0.401 

0.391 

25 

0438 

0.427 

0.415 

30 

0-445 

0.444 

0-443 

CaCl2 

20 

0.440 

0.432 

0.424 

0.413 

0.404 

0-395 

0.389 

SrCl2 

20 

0.441 

0435 

0.427 

CdCl2 

18 

0.430 

0.430 

0430 

0430 

0430 

CdBr2 

18 

0.430 

0.430 

0.430 

0.430 

0.429 

O.4IO 

0.389 

0.350 

0.222 

CdI2 

18 

0-445 

0.444 

0.442 

0.396 

0.296 

0.127 

O.O46 

0.003 

Na2SO4 

18 

0.392 

0.390 

0.383 

K2S04 

18 

0.494 

0.492 

0.490 

25 

0.496 

0.494 

0493 

T12SO4 

25 

0.478 

0.476 

H2SO4 

20 

0.822 

0.822 

0.822 

0.820 

0.8  1  8 

0.816 

0.812 

32 

0.808 

0.808 

0.808 

Ba(N03)2 

25 

. 

0.456 

0456 

0.456 

Pb(N03)2 

25 

0.487 

0.487 

MgS04 

18 

0.388 

0.385 

0.381 

0.373 

30 

0.388 

0.386 

0.380 

CdSO4 

18 

0.389 

0.384 

0-374 

0.364 

0.350 

0.340 

0.323 

0.294 

CuSO4 

18 

0-375 

0-375 

0.373 

0.361 

0.348 

0.327 

NaOH 

25 

0.201 

ELECTRICAL  CONDUCTANCE  313 

The  limiting  value  of  the  transport  numbers  with  an 
increase  in  temperature  seems  to  be  0.5,  which  indicates 
that  the  current  is  transported  by  the  cation  and  anion 
equally.  This  applies  to  all  combinations  of  cations  and 
anions. 

In  the  case  of  a  number  of  electrolytes  the  transport  num- 
bers are  abnormal  and  vary  greatly  with  the  concentration 
as  well  as  with  the  temperature.  Hittorf  found  for  aqueous 
solutions  of  cadmium  iodide  values  greater  than  unity  for 
solutions  more  concentrated  than  normal;  for  3 -normal  the 
value  for  cadmium  is  1.3,  and  for  0.03 -normal  the  value 
is  0.6 1 .  These  abnormal  values  are  explained  primarily  upon 
the  basis  of  the  formation  of  complexes  in  solution  with  or 
without  the  combination  of  the  solute  with  the  solvent.  It 
is  further  assumed  in  the  determination  of  the  transference 
number  that  there  is  no  movement  of  the  water  with  the 
electric  current,  and  in  the  case  of  concentrated  solutions 
this  is  no  longer  the  case.  By  the  introduction  of  a  substance 
which  will  remain  stationary  and  will  not  take  part  in  the 
conduction  of  the  current,  methods  have  been  devised  in 
order  to  determine  the  amount  of  water  transferred  with  the 
current  and  consequently  the  amount  associated  with  the 
different  ions. 

Kohlrausch's  Law.  —  By  employing  the  principles  that 
Wheatstone  used  in  measuring  the  resistance  of  conductors 
of  the  first  class,  Kohlrausch  devised 
a  method  for  measuring  the  con- 
ductance of  solutions.  The  ap- 
paratus, illustrated  in  Fig.  91, 
consists  of  a  wire,  AB,  provided 
with  a  scale  so  that  the  sections 
a  and  b  can  be  measured ;  the 
known  resistance  R,  and  the  elec- 
trolytic cell,  C,  into  which  the  solution,  the  resistance 
of  which  is  to  be  measured,  can  be  placed  (the  Arrhenius 


"•• 

314  PHYSICAL   CHEMISTRY 

type  of  cell  is  illustrated  in  detail  in  Fig.  92) ;  a  battery, 
B,  and  induction  coil,  /,  or  some  means  of  producing 
an  alternating  current.  T  represents  the  telephone  by 
means  of  which  the  adjustment  of  the  contact  point 
can  be  correctly  made.  By  introducing  a 
known  resistance  into  R  and  moving  the  point 
k  along  the  wire  until  the  minimum  sound 
is  obtained,  the  resistances  in  the  four  parts 
or  arms  of  the  apparatus  will  be  in  the  ratio, 

R :  Rc  =  a :  b.     Solving,  we  have  Rc  =  ^-^ , 

a 

which  gives  the  resistance  of  the  solution  in 
the  electrolytic  cell.  The  conductance  is 
the  reciprocal  of  the  resistance,  then  the 

FIG.  92.        conductance,  c  =  —  =  — — . 

RC      R  •  b 

Electrical  resistance  is  expressed  in  ohms  and  conductance 
in  reciprocal  ohms  or  mhos.  The  unit  of  conductance  is  the 
reciprocal  ohm,  the  mho.  The  specific  conductance,  *,  is 
the  conductance  of  a  cube  of  the  solution  having  sides  i  cm. 
long.  The  conductance  of  the  solution  containing  one  gram- 
equivalent  of  the  solute  when  placed  between  two  electrodes 
i  cm.  apart  and  of  such  size  as  to  contain  the  specified  volume 
of  the  solution  is  designated  the  equivalent  conductance  and 
is  represented  by  A.  Then  A  =  *V,  in  which  V  is  the 
volume  in  cubic  centimeters  which  contains  one  gram-equiv- 
alent. It  is  customary  to  employ  a  subscript  to  designate 
the  volume  of  the  solution  that  contains  one  gram-equivalent 
of  the  solute,  i.e.  AF,  which  is  the  equivalent  conductance  at 
volume  V,  and  Aw  is  the  equivalent  conductance  at  infinite  di- 
lution. The  molecular  conductance  n  is  the  conductance  of  a 
solution  containing  one  mole  of  the  solute  placed  between  two 
electrodes  i  cm.  apart  and  of  sufficient  size  to  include  the  vol- 
ume of  the  solution,  ^  =  *cV.  In  many  texts  and  journals  it 
is  customary  to  use  X  to  represent  the  equivalent  conductance. 


ELECTRICAL  CONDUCTANCE  315 

It  is  more  convenient  to  prepare  the  electrolytic  cells 
so  that  the  electrodes  are  not  exactly  i  cm.  apart,  are  not 
exactly  i  sq.  cm.  in  area,  and  do  not  inclose  a  volume  of 
exactly  one  cubic  centimeter  of  solution.  Consequently,  it 
is  necessary  to  employ  some  factor,  K,  such  that  the  value 
of  the  conductance  of  the  solution,  as  obtained  by  this  cell, 
multiplied  by  K  will  give  the  specific  conductance,  that  is, 
the  conductance  of  a  cube  of  the  liquid  one  centimeter  on  a 
side.  We  then  have,  the  conductance  of  the  solution  c 
times  K  equals  the  specific  conductance,  i.e.  cK  =  K,  and 

since  c  =  -^-,  we  have  K  =  —f-,  or  solving,  we  obtain  K  = 

Rh 

—  .     The  value  of  K,  which  is  termed  the  Cell  Constant, 
a 

may  be  readily  determined  experimentally  by  employing  in 
the  cell  a  specified  solution,  the  specific  conductance  of 
which  is  known,  determining  the  value  of  R,  a,  and  b  by  the 
Kohlrausch  method,  substituting,  and  solving  for  K.  Then 
knowing  K  for  the  particular  cell,  the  equivalent  conductance 
of  other  solutions  can  be  readily  determined  from  the  rela- 
tion A  =  K  V  which  on  substitution  of  the  value  of  K  becomes 
A  KaV 

A=^T- 

Kohlrausch  (1873-80)  by  the  above  method  made  the 
measurements  of  the  conductance  of  a  very  large  number 
of  solutions  of  different  strength.  By  dissolving  one  gram- 
molecule  and  making  it  up  to  one  liter  we  have  a  molar 
solution,  and  if  the  quantity  representing  one  gram-equiva- 
lent be  dissolved,  we  have  a  gram-equivalent  solution.  In 
the  case  of  KC1,  NaCl,  NaOH,  etc.,  these  two  kinds  of  solu- 
tions are  the  same ;  but  with  H2SO4,  BaCl2,  etc.,  one  half  a 
mole  is  required  for  a  gram-equivalent  solution,  and  hence 
these  are  one  half  the  strength  of  molar  solutions.  In  Table 
L  is  compiled  the  equivalent  conductance  A  of  aqueous 
solutions  at  18°  C.  of  many  of  the  common  acids,  bases,  and 
salts.  The  headings  of  the  columns  are  self-explanatory. 


PQ 


§0 


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i-c         ON  t>.vO  vO  t>»GO  vO  vO  !>•       W  " 


t^OO  O  rt-  (S  ONOO  t^-— ^ 


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ON(N    <N   0    ON:  ^X 


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voq^-HH   "oio^qo-oo 

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ELECTRICAL  CONDUCTANCE 


317 


1 .  From  the  data  in  this  table  it  will  be  observed  that  the 
equivalent  conductance  of  all  these  solutions  increases  with 
the  dilution,  and  it  is  found  that  the  difference  of  the  con- 
ductance for  the  first  dilutions  is  very  marked,  while  for  high 
dilutions  the  differences  are  small,  showing  that  the  values 
for  the  equivalent  conductances  are  reaching  a  limiting 
maximum  value.     That  is,  at  infinite  dilution,  which  is  ap- 
proximately 1000  liters  and  above,  the  value  for  A  becomes 
constant.     This  is  shown  in  the  following  numbers  for  NaCl, 
the  difference  being  with  increased  dilution  :    6.69  ;     4.29  ; 
3.69;    3.91;    2.33;    1.83;    1.77;    0.94;    0.79;    0.64;    0.28. 
This  shows  that  the  value  for  the  equivalent  conductance 
is  approaching  a  limiting  value. 

2.  The  additive  property  of  the  equivalent  conductance 
is  illustrated  by  the  values  given  in  Table  LI,  which  are 
obtained  from  Table  L  for  dilution  of  10,000  liters,  which  we 
may  take  as  Aw. 

TABLE  LI 


ELECTROLYTE 

AOC 

DIFFERENCE  K—  Na 

KC1 

I2Q  O7 

NaCl 

108  10 

20.97 

KNO3 

12^  5O 

NaNO3 

I  O4.  SS 

20.95 

K2SO4      .     . 
Na2SO4    .... 

130.71 
IIO  5 

20.21 

CHsCOOK                 ."•''. 

IOO  O 

CHsCOONa     .... 

76.8 

23.2 

The  difference  of  the  equivalent  conductances  for  KC1 
and  NaCl  should  be  the  same  as  the  difference  for  the 
nitrate  solutions.  This  we  find  to  be  true,  as  we  obtain  20.97 
in  one  case  and  20.95  f°r  the  other.  We  obtain  practically 


318  PHYSICAL   CHEMISTRY 

the  same  value  for  the  sulphates.  In  the  case  of  the  acetates 
the  agreement  is  not  so  marked. 

From  a  consideration  of  the  data  he  obtained,  Kohlrausch 
found  that  the  equivalent  conductance  at  infinite  dilution 
could  be  represented  by  the  sum  of  the  equivalent  conduc- 
tances of  the  cations  and  of  the  anions.  That  is,  the  migra- 
tions of  the  ions  in  solution  are  independent  of  each  other, 
and  their  combined  effect  results  in  the  conductance  of  the 
solution.  Hence  we  have  the  formulation  of  Kohlrausch 's 
Dilution  Law  of  the  independent  migration  of  the  ions  in  the 
expression  A^  =  Ac  -f  A0,  which,  stated  in  words,  is :  the 
equivalent  conductance  of  a  solution  at  infinite  dilution  is 
the  sum  of  the  equivalent  ionic  conductances,  i.e.  the  equiv- 
alent ionic  conductance  of  the  cations,  Ac,  plus  the  equivalent 
ionic  conductance  of  the  anions,  A0. 

3.  The  ratio  of  the  current  carried  by  the  cations  to  the 
total  current  is  termed  the  transference  or  transport  number 
of  the  cation,  and  similarly  we  have  the  transference  number 
of  the  anion.  These  transference  numbers  are  dependent 

on  the  velocities  of  the  ions,  and  we  have  the  relation  —  = 

na 

— ,  in  which  uc  is  the  velocity  of  the  cation  and  va   is  the 

Va 

velocity  of  the  anion.  As  the  total  equivalent  conductance 
is  the  sum  of  the  equivalent  ionic  conductances,  it  follows 

that  the  relation  ^  =  A£  holds,  and  therefore  ^  =  ^ .    Add- 

va      A0  na      Aa 

ing  unity  to  both  sides  of  the  equation  we  obtain  —  +  i  = 

na 

^+  i,  which  becomes  n°  +  Ha  =  AC  +  Aq,  and  remember- 
Aa  na  Aa 

ing  that  nc  +  na  =  i,  and  Ac  +  A0  =  A^-,  we  have  on  sub- 
stitution —  =  — *  .     Solving  for  A0  we  have  A0  =  naAx,  and 
na      Aa 

similarly  we  may  also  obtain  Ac  =  nc Aw . 


ELECTRICAL  CONDUCTANCE  319 

We  may  now  apply  this  to  a  specific  problem  as  an  illus- 
tration. 

The  equivalent  conductance  A^  at  infinite  dilution  of  NaCl 
is  109  mhos,  and  this  for  NaCl  is  also  the  molar  conductance, 
/u,M.  The  transport  number,  na  for  the  anion,  the  chlorine 
ion,  is  0.615.  Substituting  these  values  in  the  equation  we 
have  A0  =  0.615  X  109,  or  A0  =  67,  the  equivalent  ionic  con- 
ductance of  chlorine.  The  equivalent  ionic  conductance  of 
the  sodium  ion  is  109  —  67  =  42,  or  substituting  in  the  equa- 
tion above,  Ac  =  WcA^,  is  Ac  =  (1—0.615)  109,  and  Ac=42. 
It  is  apparent  that  if  the  transference  number  of  one  ion  is 
known,  then  the  ionic  conductance  of  it  and  of  the  one  with 
which  it  is  associated  may  be  readily  calculated.  Above  we 
have  determined  the  equivalent  ionic  conductance  for  Na  and 
Cl.  Now  if  we  determine  experimentally  the  equivalent 
conductance,  Aw,  for  NaNOs,  we  have  from  Kohlrausch's 
Law,  A^  =  ANa  +  ANOS>  and  since  we  know  A^  and  ANa, 
we  can  solve  for  ANO  ,  the  equivalent  ionic  conductance  of 

3 

NOs.  By  the  proper  combinations  it  is  possible  to  determine 
the  ionic  conductance  for  any  of  the  ions.  These  values  of  the 
equivalent  conductances  of  the  separate  ions  at  18°  C.  have 
been  accurately  determined,  and  the  values  compiled  by 
Noyes  and  Falk  are  given  in  Table  LII. 

From  the  values  of  the  equivalent  conductances  of  the  ions 
and  assuming  that  Kohlrausch's  Dilution  Law  holds,  it  is 
then  possible  to  calculate  the  equivalent  conductance  at  in- 
finite dilution,  A^,  for  any  electrolyte.  This  gives  us,  then, 
the  equivalent  or  the  molecular  conductance  at  infinite  dilu- 
tion, and  Ostwald  has  proposed  that  the  conductance  at  any 
moderate  dilution  could  be  represented  byA  =  a(Ac  +  Aa) 
where  a  is  the  fractional  part  the  equivalent  conductance  at 
any  dilution  is  of  the  equivalent  conductance  at  infinite  dilu- 
tion. Since  A^  =  Ac  +  A0,  then  A  =  aAw,  or  solving  for  a 

we  have  a  = 

AOQ 


-      320 


PHYSICAL  CHEMISTRY 


TABLE  LII  —  EQUIVALENT  IONIC  CONDUCTANCES  OF  THE 
SEPARATE  IONS 

(Noyes  and  Falk— Jour.  Am.  Chem.  Soc.,  34,  479  (1912)) 


VALUES  AT  18°  C. 

VALUES  AT  25°  C. 

Cs 

68.0 

Ba 

554 

Br 

67.7 

Tl 

76.0 

I 

76.5 

Rb 

67-5 

Ca 

51-9 

I 

66.6 

K 

74.8 

Cl 

75-8 

Tl 

65-9 

Sr 

51-9 

Cl 

65-5 

Ag 

634 

NO3 

70.6 

NH4 

64.7 

Zn 

47.0 

NO3 

61.8 

Na 

5i-2 

Br03 

54-8 

K 

64-5 

Cd 

46.4 

SCN 

56.7 

H 

350.0 

OH 

196.0* 

Ag 

54-0 

Mg 

45-9 

C1O3 

55-1 

Pb 

71.0 

SO4 

80.0 

Na 

434 

Cu 

45-9 

BrO3 

47.6 

Ba 

65-2 

C204 

72.7 

Li 

33-3 

La 

61.0 

I03 

34-0 

Ca 

60.0 

C2H302 

40.8* 

H 

314.5 

F 

46.7 

Mg 

55-0 

Fe(CN)6f 

110.5 

Pb 

60.8 

S04 

68.5 

La 

72.0 

C2H30 

35-* 

NH4 

74-8* 

C204 

63.0 

Fe(CN)6t 

95-0 

OH 

174-* 

*  From  Kohlrausch's  values  at  18°.     These  values  for  25°  are  cal- 
culated from  1 8°  values  and  the  temperature  coefficients  given, 
t  Ferrocyanide  ion. 


CHAPTER  XXVIII 
ELECTROLYTIC  DISSOCIATION 

FROM  the  equivalent  conductance  of  solutions  compiled 
in  Table  L,  it  will  be  seen  that  the  only  substances  listed 
are  acids,  salts,  and  bases.  It  has  also  been  found  that  the 
only  aqueous  solutions  that  conduct  the  electric  current  are 
solutions  of  these  three  classes  of  substances,  which  are  termed 
electrolytes.  It  has  also  been  shown  that  it  was  these  same 
three  classes  of  substances  which  in  aqueous  solutions  gave 
abnormal  values  for  (i)  the  osmotic  pressure,  (2)  the  lower- 
ing of  the  vapor  pressure,  (3)  the  lowering  of  the  freezing 
point,  and  (4)  the  rise  of  the  boiling  point.  If  342  grams  of 
cane  sugar  are  dissolved  in  water  and  made  up  to  one  liter 
we  have  a  molar  solution.  A  molar  solution  of  grape  sugar 
will  contain  180  grams.  The  osmotic  pressures  of  these 
two  solutions  are  the  same,  the  vapor  pressures  are  the  same, 
the  freezing  points  are  the  same,  and  the  boiling  points  are 
the  same.  That  is,  one  gram-molecule  of  any  substance, 
such  as  these,  will  produce  the  same  lowering  of  the  vapor 
pressure  of  the  solvent,  whatever  the  difference  in  the 
formula  weights  may  be.  It  is  the  same  number  of  moles  of 
the  different  solutes  that  causes  the  same  change  of  the 
boiling  points,  the  same  lowering  of  the  freezing  points  and 
of  the  vapor  pressures,  when  dissolved  in  the  same  amounts 
of  the  same  solvent.  If  we  have  the  same  number  of  moles 
of  different  solutes  dissolved  in  the  same  quantity  of  solvent, 
the  osmotic  pressures  of  all  the  solutions  will  be  the  same. 

321 


322  PHYSICAL   CHEMISTRY 

Those  properties  such  as  the  osmotic  pressure,  the  lowering 
of  the  vapor  pressure,  the  rise  of  the  boiling  point,  etc.,  which 
depend  upon  the  number  of  moles  or  parts  in  solution,  are 
designated  Colligative  Properties.  The  relative  magnitudes 
of  the  values  are  proportional  to  the  number  of  moles  of 
solute. 

It  was  shown  in  the  discussion  of  osmotic  pressure  meas- 
urements that  a  large  number  of  substances  gave  abnormal 
values  for  the  osmotic  pressure  and  that  van't  Hoff  proposed 
to  introduce  a  correcting  factor  i  in  the  formula  to  take  care 
of  these.  The  formula  then  took  the  form  p0  V  =  iR  T,  in 
which  i  is  the  number  of  times  larger  the  osmotic  pressure 
found  is  than  it  should  be  on  the  basis  of  the  formula  weight 
of  the  solute.  The  value  of  i  is  then  the  value  of  the  ratio  of 
the  number  of  moles  present  to  the  number  which  corresponds 
to  the  formula  weight  ;  this  is  on  the  basis  that  the  osmotic 
pressure  is  a  colligative  property. 

Similarly  we  have  seen  that  the  vapor  pressures  of  solutions 
of  salts,  acids,  and  bases  are  much  lower  than  they  should  be. 
In  Table  XLVIII  the  last  columns  show  that  the  rise  of  the 
boiling  point  of  some  solutions  is  two  and  in  some  cases  three 
times  what  the  changes  should  be.  From  these  values  we  may 
obtain  the  ratio  of  the  number  of  moles  necessary  to  produce 
this  pressure  to  the  number  of  molecules  represented  by  the 
formula  weight,  i.e.  the  value  i  of  van't  Kofi's  formula,  or 
as  sometimes  called,  van't  HofT's  coefficient.  If  g  grams  of 
the  solute  produces  a  lowering  of  A  degrees  when  dissolved  in 
100  grams  of  the  solvent,  the  formula  weight,  m,  will  produce 


a  lowering  of     —  degrees,  and  as  the  gram-molecular  lower- 
g 

wA 

ing  is  1  8.  6°,  it  follows  that  i  =    /  0- 

lo.O 

Arrhenius  recognized  that  the  aqueous  solutions  of  acids, 
bases,  and  salts  also  conduct  the  electric  current.     He  formu- 


ELECTROLYTIC   DISSOCIATION  323 

lated  the  Electrolytic  Dissociation  Theory  in  order  to 
account  for  the  extra  number  of  moles  present  in  these  aque- 
ous solutions  which  apparently  produce  these  abnormal 
values  of  the  osmotic  pressure,  the  lowering  of  the  vapor 
pressure,  the  lowering  of  the  freezing  point,  and  the  eleva- 
tion of  the  boiling  point.  We  saw  that  Clausius  in  his  expla- 
nation of  the  passage  of  electricity  assumed  that  there  were  a 
few  ions  in  solution  resulting  from  the  bombardment  and 
collision  of  the  polarized  molecules.  Arrhenius  went  con- 
siderably farther  and  assumed  that  a  large  part  of  the  solute 
existed  in  the  ionic  form  and  that  through  the  mere  act  of 
solution  the  solute  is  separated  into  its  ions,  that  is,  the  solute 
is  dissociated.  •  Arrhenius  assumed  that  the  solute  exists  in 
solution  in  two  ways,  part  of  it  as  active  and  part  inactive, 
the  active  part  being  the  part  dissociated,  existing  as 
ions,  and  the  inactive  part  being  the  part  remaining 
undissociated. 

On  dissolving  sodium  chloride  in  water  we  would  then 

have  NaCl  ^  Na+  -  Q- 

inactive  ^±  active 

the  inactive  sodium  chloride  being  in  equilibrium  with  the 
active  part,  which  is  the  part  ionized  and  existing  as  Na  and 
Cl  ions.  The  relative  quantities  of  the  active  and  inactive 
parts  of  the  molecule  depend  upon  the  dilution.  As  water 
is  added,  the  amount  of  dissociation  increases,  while  if  the 
concentration  of  the  salt  is  increased,  the  inactive  part  in- 
creases, and  the  dissociation  decreases.  To  these  dissociated 
or  active  parts  in  solution  Arrhenius  gave  the  term  ions,  re- 
taining the  term  introduced  by  Faraday  to  represent  that 
which  conducted  the  electric  current.  He  further  showed 
that  one  gram-equivalent  of  the  ions  which  migrated  to  the 
cathode  carried  96,540  coulombs  or  onefaraday  of  electricity, 
and  the  ions  which  migrated  toward  the  anode  carried  a 
charge  of  96,540  coulombs  of  electricity  but  of  the  opposite 


••• 

324  PHYSICAL   CHEMISTRY 

sign.  It  was  recognized  that  the  dissociated  parts,  the  ions, 
are  not  like  the  metallic  sodium  and  the  elemental  chlorine, 
but  that  they  are  decidely  different,  and  this  difference  is 
due  to  the  difference  of  their  energy  content,  for  when  the 
ions  reach  the  electrodes  in  the  processes  of  electrolysis  they 
give  up  their  electrical  charge  and  become  the  elemental  sub- 
stances. The  ionic  form  differs  from  the  elemental  form  in 
that  the  ions  carry  charges  of  electricity  ;  the  cations  positive 
charges  and  the  anions  negative  charges.  The  sodium  ion  is 
represented  thus,  Na+,  the  symbol  for  sodium  with  a  small 
plus  sign  indicating  that  the  electrical  charge  is  positive  and 
that  on  each  gram-equivalent  of  ions  there  is  a  positive  charge 
of  96,540  coulombs.  The  chlorine  ion  is  -expressed  Cl~, 
the  negative  sign  indicating  a  negative  charge  of  96,540 
coulombs  of  electricity  residing  on  one  gram-equivalent 
of  chlorine  ions.  The  difference  between  the  atomic  and 
ionic  form  is  then  merely  a  difference  in  their  energy 
content. 

The  dissociation  of  acids  results  in  the  formation  of  hydro- 
gen ions  and  the  ion  of  the  acid  part  or  radical  thus  :  H+  •  Cl~  ; 
H+  -  H+  •  SO4— ;  H+  •  NO3-  ;  CH3COO-  •  H+.  From  the  dis- 
sociation of  bases  we  have  the  basic  ion  and  the  hydroxyl 
ions ;  thus,  Na+  •  OH~  ;  NH4+  •  OH-  ;  Ba++  •  OH-  •  OH-  ; 
while  in  the  case  of  salts  we  have  the  part  that  takes  the 
place  of  the  hydrogen  in  acids  and  the  acid  part  of  the  com- 
pound ;  thus,  K+  •  Cl-  ;  Sr+  •  N03~  •  NOr  ;  Na+  •  C2H3O2- ; 
etc.  The  dissociation  into  ions  is  the  same  as  the  separation 
which  takes  place  in  chemical  reactions.  In  fact,  some  go 
so  far  as  to  state  that  all  reactions  are  ionic,  hence,  the  react- 
ing parts  and  the  parts  which  go  from  one  compound  to 
another  are  those  which  in  aqueous  solutions  are  recognized 
as  the  ions. 

It  was  shown  by  Kohlrausch  and  confirmed  subsequently 
that  the  conductance  is  the  sum  of  the  ionic  conductances, 
and  hence  the  maximum  equivalent  conductance  must  be 


ELECTROLYTIC  DISSOCIATION  325 

attained  when  the  electrolyte  is  completely  dissociated. 
Ostwald  showed  that  the  conductance  at  any  other  dilution 

could  be  represented  by  A  =  o:(Ac  +  A0)  or  - — - — —  =  a,  or 

Ac  +  Aa 

—  =  a,  which  is  the  ratio  of  the  conductance  at  the  given 

AOO 

dilution  to  the  conductance  at  infinite  dilution,  a  is  called 
the  Degree  of  Dissociation.  We  saw  when  we  were  studying 
the  dissociation  of  gases  that  a  relation  between  the  degree 
of  dissociation  a  and  i  was  expressed  as  follows :  i  —  i  + 

(/  —  i)a  or  a  =  — — .     The  factor  i  is  the  ratio  of  the  total 

/—  J 
number  of  parts  present  after  dissociation  to  the  original 

number.     The  original  number  of  parts  is  defined  by-^  =  n, 

in  which  g  is  the  weight  in  grams,  m  is  the  formula  weight, 
and  n  is  the  number  of  gram-molecules  or  moles.  The  value 
for  a.  can  be  obtained  from  the  electrical  conductivity 
methods  ;  van't  HofT  showed  that  the  value  for  i  could  be  ob- 
tained from  osmotic  pressure  data. 

We  have  seen  that  the  freezing  point,  boiling  point,  and 
vapor  pressure  methods  all  give  abnormal  values  for  the 
molecular  weight  of  the  solute,  and  from  these  the  value 
of  i  can  be  calculated.  Then  from  the  above  relation  be- 
tween i  and  a  the  value  for  i  can  be  calculated,  providing 
a  is  known  and  /,  the  number  of  parts  into  which  the  dis- 
solved electrolyte  is  dissociated.  Arrhenius  did  this,  tak- 
ing the  best  data  available  at  that  time  (1887),  and  found 
that  the  values  for  i'  calculated  by  the  two  methods  agreed 
fairly  well.  He  concluded  that  the  value  for  i  could  be 
ascertained  from  any  of  the  five  methods;  viz.  osmotic 
pressure,  boiling  point,  freezing  point,  vapor  pressure, 
and  electrical  conductivity.  Hence  it  follows  that  all 
of  them  carl  be  used  for  the  determination  of  <*,  the  degree  of 
dissociation. 


TABLE  LIII  —  DEGREE  OF  DISSOCIATION 


METHOD 

LITERS  PER  GRAM  EQUIVALENT 

200 

100 

50 

20 

10 

5 

2 

KCl 

F.  P. 
Cond. 
F.  P. 
Cond. 
F  P 

96.3 
95-6 
94-7 

95-3 
95-3 

95-4 
94-4 
94-9 

95-5 
95-0 
95-3 
95-2 

95-4 
94.1 
94-6 
93-9 
93-9 
93.8 
96.8 
99-1 
98.1 
97-4 

89.9 

91.0 
91.0 
80.3 
74-9 

67.5 
94-8 
91.7 
91.7 
89.8 
89.0 
88.6 
92.9 
90.5 

89-3 
69.4 
74-0 
61.6 
70.9 
66.5 
71.0 
65.8 
69.4 
89.4 
86.9 

94-3 
94.1 
92.8 
94.1 
93-8 
93-6 

93-7 
93-7 
93-2 

94.0 
9<M 
93-2 
90.1 
93-5 
91.4 
93-3 
91.4 
93-4 
9i-3 
92.8 
91.6 
91.7 
92.1 
9S-i 
97-5 
97-2 
96.0 
97-o 
87.8 
88.3 

88.3 

88.3 
79.1 
73-5 
78.0 
66.1 
59-3 
57-3 
92.1 
87.1 
88.8 
86.1 
85.0 
84.5 
89.9 
87.2 

85.7 
61.8 
66.9 
54-5 
62.9 
58.2 
63-3 
56.9 
61.4 
86.8 
82.7 

91.8 
92.2 
90.7 
92.1 
92.2 
91.6 
93-0 

92.8 
89.0 
92.9 
92.1 
88.5 
91.0 
88.0 
91.1 
89.1 
91.0 
89.1 
91.0 
88.2 
90.3 
89.0 
89.0 
91-3 
93-0 
95-7 
96.2 
94-2 

85-5 
85.0 
87.6 
85.1 
88.5 
85.1 
76.8 
66.4 
70.4 
57-3 
54-o 
46.9 
90.1 
84.8 
85.5 
81.8 
80.4 
79-3 
85.7 
83.2 
86.7 

53-6 
59-6 
45-5 
55-0 
48.9 
55-6 
47-7 
53-4 
77-8 

88.5 
88.9 
87.8 

89^2 

91.2 
87.8 
88.9 
88.8 
85.5 
87.1 
83.6 
86.7 
84.9 
86.6 
84-9 
86.8 
82.8 
86.0 
84.2 
84.2 

93-3 
94-4 
91.2 
94-o 
81.9 
79-8 
83.7 
80.3 
85.4 
80.3 
69.0 
55-9 
S8.9 

40.0 

88.7 
79-2 

74-4 
72.4 
70.8 
78.5 
77.1 
79-5 
75-6 
42.0 
50.6 
31-8 
45-5 

46.4 
34-3 
43-7 

634 
59-1 

86.1 
86.0 
85.6 

87-5 
85.2 
86.3 
84.7 
90.1 
84.6 
86.3 
85-9 
83.0 
83.2 
78.1 
82.4 
79-8 
79-9 
79-8 

76.5 
81.9 
77-3 
80.1 

91.7 
90.0 

78.8 
75-9 
81.5 
76.4 
83-9 
76.5 
60.5 
45-3 
48.2 

22.5 

88.4 
73-1 

67.9 
64.9 
63.5 
73-0 
72.2 
73-6 
70.4 
32.4 
44-9 

39-6 
40.5 
37-7 

58.1 
53-8 

83.3 
82.7 
83-2 

85.0 
81.8 
82.9 

81.2 
83.9 
82.5 
79-8 
78.8 
71.1 
77.2 

78.0 

77-5 
75-2 

87.9 

75-8 
72.0 
80.4 
72.7 
83.3 
72.8 
53-9 
37-5 
36.7 

IO.O 

68.4 

60.9 
56.8 
55-9 

67^3 
67.2 
65.2 
22.3 
40.3 

35-i 
36.0 

33-2 

52.0 
49-8 

80.0 

77-9 

82.4 
77-3 
77.8 

76.6 
81.3 
76.6 

71.9 
68.8 
70.3 

67.2 
68.8 
68.7 
28.9 

62.8 

50.4 
42.7 
45-4 
56.8 
61.8 
56.7 

8.4 

29.0 
42.5 

NHiCl 

NaCl 

CsCl      

Cond. 
F.  P. 
Cond. 
F.  P. 
Cond. 
F.  P. 
Cond. 
F.  P. 
Cond. 
F.  P. 
Cond. 
F.  P. 
Cond. 
F  P 

LiCl  

KBr 

NaNOs  

KNOs    ,    ,    
KClOa 

KBrOs             .                   .     . 

KIOs      
NalOs    
KMn04  
HC1 

Cond. 
F.  P. 
Cond. 
F.  P. 
Cond. 
F.  P. 
Cond. 
F.  P. 
Cond. 
F.  P. 
Cond. 
F.  P. 
Cond. 
F.  P. 
Cond. 
F.  P. 
Cond. 
F  P 

HNOs 

BaCU     
CaClz 

MgCU    
CdCb     .... 

CdBr2    

Cond. 
F.  P. 
Cond. 
F.  P. 
Cond. 
F.  P. 
Cond. 
F.  P. 
Cond. 
F  P 

CdI2  

Cd(NOs)2    

Ba(NCh)2 

Pb(NCH)2    

K2S04       ,-/, 

Na<S04  *    » 

Cond. 
F.  P. 
Cond. 
F  P 

MgS04  

Cond. 
F  P 

CuSO4    

Cond. 
F  P 

ZnSO4    

Cond. 
F.  P. 
Cond. 
F  P 

CdSO4 

K3Fe(CN)6                              .    . 

Cond. 
P.P. 
Cond. 
F.  P. 
Cond. 

K4Fe(CN)6      

326 


ELECTROLYTIC  DISSOCIATION  327 

In  Table  LIII  are  given  data  compiled  by  Noyes  and  Falk 
which  are  supposed  to  be  the  best  available,  and  from  these 
it  is  apparent  that  Arrhenius  was  justified  in  his  conclusion 
that  the  degree  of  dissociation  is  practically  the  same  when 
determined  fromT  the  lowering  of  the  freezing  point  and  from 
the  electrical  conductance  of  the  solution,  although  the 
former  is  determined  at  o°  C.  and  the  latter  at  18°  C.  From 
the  data  available  Arrhenius  pointed  out  many  discrepancies 
and  called  special  attention  to  the  sulphates.  For  the  sul- 
phates of  the  alkalies  the  values  for  the  degree  of  dissociation 
vary  several  per  cent,  while  in  the  case  of  CuSO4,  ZnSO4,  CdSO4, 
etc.,  the  variation  according  to  the  data  in  this  table  is  very 
marked,  amounting  in  some  cases  to  10  or  1 2  per  cent.  In  the 
case  of  MgSO4,  at  the  dilution  of  5  liters,  according  to  the 
freezing  point  method,  the  value  of  a  is  22.3,  while  by  the 
electrical  conductance  40.3  was  found. 

The  value  for  the  degree  of  dissociation  of  K2SO4  is  89.9  in 
solutions  in  which  one  gram-equivalent  is  contained  in  100 
liters.  Taking  this  value  as  90  per  cent,  what  will  be  the 
value  of  i?  The  electrolyte  dissociates  according  to  this 
equilibrium  equation,  K2SO4  ^±  K+  •  K+  •  SO4~  ~,  i.e.  it  dis- 
sociates into  three  parts,  and/  then  =  3.  The  relation  is 

1  =  i  +  (/  —  i)a.     Substituting  these  values  for  /  and  a, 
we   have   i  =  i  +  (3  —  1)0.9.     Solving,  i  =  2.80,  that   is, 
there  are  2.8  times  as  many  parts  in  the  solution  after  it  is 
90  per  cent  dissociated  as  before  dissociation.     In  case  of 
complete  dissociation  a  is  one,  or  the  degree  of  dissociation 
100  per  cent.     Then  substituting  in  the  formula,  we  have 
*  =  i  +  (3  —  1)1,  and  i  =  3,  the  number  of  times  the  total 
number  of  parts  is  of  the  original  number  of  molecules.     This 
is  apparent  from  an  inspection  of  the  equilibrium  equation ; 
if    we    have   one   mole    of  K2SO4,  and  it  dissociates  into 

2  K+  and  one  SO4~  ~,  there  are  three  times  as  many  parts 
(ions  in  this  case)  as  there  were  of  the  original  number 
of  molecules. 


* 

328  PHYSICAL  CHEMISTRY 

An  examination  of  the  values  of  the  equivalent  conduct- 
ances given  in  Table  XL  VI 1 1  shows  that  the  values  for  the 
acids  HC1,  HNO3,  and  H2SO4  are  very  high  as  compared  with 
the  values  of  the  other  electrolytes  ;  the  values  for  the  bases, 
KOH  and  NaOH,  are  next  in  size ;  while  the  values  for  the 
salts  of  the  alkalies  are  next  in  magnitude.  Since  the  speeds 
of  the  H  and  OH  ions  are  the  most  rapid,  we  expect  solutions 
containing  them  to  be  the  best  conductors.  Such  is  the  case, 
and  in  general  acids  are  the  best  conductors,  bases  next,  and 
salts  of  the  alkalies  are  all  good  conductors.  It  will  be  ob- 
served, however,  in  the  case  of  acetic  acid,  that  the  value  of 
the  equivalent  conductance  is  only  about  one  tenth  that  of 
the  other  acids,  yet  each  solution  contains  the  same  gram- 
equivalent  of  hydrogen.  Similarly,  solutions  of  NH4OH 
are  very  poor  conductors,  the  value  of  AIQO  being  7.1  as 
against  203  for  NaOH  and  228  for  KOH,  yet  there  is  the 
same  quantity  of  OH  by  weight  in  the  solutions.  How,  then, 
is  the  difference  in  the  conductance  accounted  for?  Since 
the  current  is  carried  by  the  ions,  we  assume  that  there  is 
not  the  quantity  of  H  ions  in  a  solution  of  acetic  acid  that 
there  is  in  the  HC1  solution,  nor  are  there  the  OH  ions  in  the 
solution  of  NH4OH  that  there  are  in  the  NaOH  solution. 
Since  these  ions  come  from  the  dissociation  of  the  electro- 
lytes, we  conclude  they  are  very  slightly  dissociated.  In 
different  ways  the  strength  of  the  different  acids  can  be  de- 
termined, and  they  all  give  values  showing  that  acetic  acid 
is  a  weak  acid  as  compared  to  HC1.  It  is  concluded  that 
those  acids  that  are  highly  dissociated  and  yield  a  large  num- 
ber of  hydrogen  ions  are  strong  acids  and  the  slightly  disso- 
ciated acids  are  weak  acids.  The  same  holds  true  for  bases  ; 
NH4OH  is  therefore  a  weak  base.  Upon  the  basis  of  this  we 
may  formulate  the  following  definitions :  An  acid  is  a  sub- 
stance which  in  an  aqueous  solution  yields  hydrogen  ions. 
A  base  is  a  substance  which  in  an  aqueous  solution  yields 
hydroxyl  ions.  Electrolytes  in  general  may  be  classified  into 


ELECTROLYTIC  DISSOCIATION  329 

strong  electrolytes  or  those  which  in  aqueous  solutions  are 
highly  dissociated,  and  weak  electrolytes  or  those  which  are 
but  slightly  dissociated.  The  salts  of  the  alkalies  and  of  the 
alkaline  earths  are  more  than  80  per  cent  dissociated  in  dilu- 
tions greater  than  100  liters  and  the  sulphates  of  the  heavy 
metals  are  only  about  50  to  60  per  cent  dissociated,  and 
the  weak  electrolytes,  such  as  the  weak  acids  and  bases,  are 
less  than  25  per  cent  dissociated. 

The  question  arises,  how  can  the  equivalent  conductance 
be  obtained  in  the  case  of  weak  electrolytes  ?  Suppose  the 
equivalent  conductance  at  infinite  dilution,  A^,  of  acetic 
acid,  CH3COOH,  is  to  be  obtained.  Acetic  acid  is  so 
slightly  dissociated  that  the  value  at  infinite  dilution  cannot 
be  determined  experimentally.  The  value  for  H+  can  be 
obtained  from  the  completely  dissociated  HC1  providing  the 
equivalent  ionic  conductance  of  Cl+  is  known.  Then  in  a 
similar  way  by  taking  a  solution  of  an  alkali  acetate-  such  as 
CH3COONa,  the  maximum  value,  A^,  can  be  obtained  ex- 
perimentally since  it  is  a  strong  electrolyte.  From  Kohl- 
rausch's  Law  we  have  A^  =  Ac  +  Aa.  From  Table  L  we 
find  the  value  of  the  equivalent  ionic  conductance  of  Cl~ 
at  1 8°  C.  is  65.5,  and  if  A^  for  HC1  is  377,  then  we  have 
377  ~  65.5  =  311.5  as  the  value  of  the  equivalent  ionic 
conductance  of  H+.  Similarly  for  CH3COONa  we  have 
A^  =  76.8,  and  the  equivalent  ionic  conductance  of  Na+ 
is  43.4 ;  then  the  value  for  the  acetate-ion  is  76.8  —  43.4  = 
33.4.  The  value  of  A^  for  acetic  acid  is  then  311.5  +33.4  = 
344.9,  but  the  value  at  the  dilution  100  liter  is  AIM  =  14-3, 

and  the  degree  of  dissociation  is  — ^  =     I4'^  =4.1  percent. 

A«,       344-9 

There  are  a  number  of  interesting  properties  of  solutions 
which  are  attributed  to  the  properties  of  the  ions,  and  many 
of  these  have  been  put  forth  as  confirmatory  evidence  in 
favor  of  the  theory  of  electrolytic  dissociation.  The  theory 
has  been  applied  to  explain  many  phenomena  and  particularly 


/*• 

330  PHYSICAL  CHEMISTRY 

in  qualitative  analysis.  We  shall  present  a  few  of  the  more 
general  and  commonly  accepted  applications  of  the  elec- 
trolytic dissociation  theory  in  order  to  emphasize  the  method 
of  using  it  to  explain  the  properties  of  solutions  and  chemical 
reactions. 

i.  Effect  of  temperature  on  the  conductance  is  shown  in 
Table  L,  in  which  is  given  the  equivalent  ionic  conductances 
of  the  separate  ions.  For  example,  the  value  for  K  at  18° 
is  64.5,  while  at  25°  it  is  74.8  mhos,  thus  showing  a  marked 
increase  in  the  ionic  conductances  with  the  temperature. 
The  equivalent  conductances  of  the  electrolytes  then  increase 
with  the  increase  in  the  temperature,  and  tables  have  been 
compiled  showing  the  temperature  coefficient  of  the  con- 
ductance of  a  large  number  of  electrolytes.  The  transport 
numbers  also  vary  with  the  temperature,  as  is  shown  in  Table 
XLIX.  As  the  conductance  is  proportional  to  the  speed  of 
the  ions,  the  equivalent  conductance  is  proportional  to  the 
number  of  these  which  are  transporting  the  current.  It  fol- 
lows then  that  in  order  to  determine  the  effect  of  temperature 
upon  the  degree  of  dissociation  a  number  of  factors  will  have 
to  be  taken  into  consideration.  In  addition  to  the  number 
resulting  from  the  dissociation  their  speed  will  be  influenced 
by  the  viscosity  of  the  solution,  that  is,  to  the  friction  which 
the  ions  encounter  in  their  passage  through  the  solution,  which 
varies  with  the  temperature.  The  thermal  change  accom- 
panying the  ionization  is  termed  the  heat  of  ionization,  and 
Arrhenius  calculated  this  from  the  rate  of  change  of  conduct- 
ance with  the  temperature.  The  heat  of  ionization,  while 
it  may  be  either  positive  or  negative,  is  usually  positive, 
which  means  that  the  ionization  is  accompanied  with  evolu- 
tion of  heat,  and  according  to  Le  Chatelier's  theorem  the 
ionization  should  decrease  with  a  rise  in  temperature.  The 
heat  of  ionization  may  be  determined  from  the  constant  of 
the  heat  of  neutralization  and  from  the  law  of  thermal  neu- 
trality, reference  to  which  will  be  made  subsequently,  but  it 


ELECTROLYTIC  DISSOCIATION 


331 


would  lead  us  too  far  to  develop  the  thermodynamic  formula 
for  calculating  the  influence  of  temperature  on  the  degree  of 
ionization. 

2.  Basicity  of  organic  acids  has  been  shown  by  Ostwald 
to  bear  a  definite  relation  to  the  equivalent  conductance  of  the 
sodium  salts  of  the  acid  at  32  and  1024  liters  dilution.  For 
monobasic  acids  this  difference  is  10  units,  and  as  the  basicity 
increases  the  differences  are  found  to  be  multiples  of  10. 

That  is,  Al024  ~  Aa2  =  the  basicity  of  the  organic  acid.     In 


10 


Table  LIV  from  data  according  to  Ostwald  is  given  the 
difference  in  the  equivalent  conductance  of  the  sodium  salts 
of  a  number  of  organic  acids,  and  in  the  last  column  the 
basicity  as  calculated  from  the  above  formula. 

TABLE  LIV 


SODIUM  SALT 

(A1Q24-A32) 

DIFFERENCE 

BASICITY 

Sodium  nicotinate 

78  8   68  4 

IO  d 

I 

Sodium  quinolinate  

90.0  69.2 

20.8 

2 

Sodium  pyridinetricarbonate  . 

113.1    82.1 

31.0 

3 

Sodium  pyridinetetracarbonate    . 

I2I.2    80.8 

40.4 

4 

Sodium  pyridinepentacarbonate  . 

127.8    77.7 

50.1 

5 

3.  Additive  Properties.  We  have  seen  that  some  prop- 
erties of  substances  were  attributed  to  permanent  charac- 
teristics of  the  elements,  and  that  the  sum  of  these  gave  the 
properties  of  the  substances,  such  as  the  atomic  volume, 
atomic  heat,  index  of  refraction,  magnetic  rotatory  power, 
etc.  These,  however,  we  saw  were  only  approximations  at 
best,  but  in  solutions  of  electrolytes  these  additive  relations 
appear  to  be  much  more  exact.  Very  extended  data  have 
been  presented  by  MacGregor,  Groshaus,  Ostwald,  Gladstone, 
and  numerous  other  authors,  in  which  they  emphasize  the 
additive  properties  of  solutions  of  electrolytes,  and  even 


332  PHYSICAL  CHEMISTRY 

before  the  formulation  of  the  electrolytic  theory  many  ob- 
servers attributed  the  properties  of  the  solution  to  the  inde- 
pendent characteristic  properties  of  the  constituents  of  the 
solute. 

Whetham  calls  attention  to  the  following  relations  which 
emphasize  the  additive  properties  of  solutions  of  electrolytes. 
When  ionization  is  complete,  the  properties  of  the  solution 
should  be  the  additive  result  of  the  individual  properties 
of  the  ions  and  of  the  solvent,  and  when  dissociation  is  not 
complete,  there  should  appear  an  additive  factor  due  to  the 
undissociated  solute.  The  specific  gravities  of  salt  solutions 
were  calculated  by  Valson  from  experimentally  determined 
moduli  of  the  elements.  By  the  specific  volume  relations 
Groshaus  showed  that  the  molecular  volume  of  the  solute  is, 
in  dilute  solutions,  the  sum  of  two  constant  factors,  one  for 
the  acid  and  the  other  for  the  base.  That  the  densities  and 
thermal  expansions  of  solutions  are  also  additive  has  been 
confirmed  by  Bender.  The  volume  change  accompanying  the 
neutralization  of  acids  by  bases  also  illustrates  the  additive 
properties  as  shown  by  Ostwald  and  by  Nicol. 

The  additive  character  of  colored  solutions  is  readily 
seen  from  an  examination  of  the  absorption  spectra  of  a  series 
of  such  solutions  containing  a  common  ion,  the  absorption 
spectra  due  to  this  ion  being  unaffected  by  the  other  parts 
of  the  solute  in  solution.  In  aqueous  solutions  anhydrous 
cobalt  chloride  forms  solutions  red  in  color  while  the  pure 
salt  itself  is  blue.  The  color  of  the  cobalt  ion  is  then  red. 
In  alcoholic  solutions,  in  which  the  dissociation  as  obtained 
from  the  conductance  is  practically  negligible,  the  color  of 
the  solution  is  blue — the  color  of  the  undissociated  compound. 
Upon  addition  of  water  to  this  solution  the  red  color  gradu- 
ally appears.  Copper  ions  are  blue,  hence  all  aqueous  solu- 
tions of  copper  salts  should  be  blue.  If,  however,  we  add 
KCN  to  an  ammoniacal  copper  sulphate  solution,  we  have 
the  solution  completely  decolorized  with  the  formation  of 


ELECTROLYTIC   DISSOCIATION  333 

K3Cu(CN)4  and  the  complete  disappearance  of  copper  ions. 
K2CrO4  dissociates  into  2  K+  •  CrO4  and  forms  yellow 
aqueous  solutions  ;  hence  the  CrO4  ion  is  yellow ;  as  solutions 
of  salts  of  the  alkalies  are  colorless,  their  ions  are  colorless. 
If  the  chromate  is  reduced  by  H2S,  we  obtain  a  greenish  solu- 
tion with  the  formation  in  the  presence  of  H2SO4  of  Cr2  (864)3, 
which  dissociates  as  follows:  2  Cr+  +  4"  •  3  SO4  .  Since  the 
864  ions  are  colorless,  the  green  color  of  the  solution  is  attrib- 
uted to  the  green  color  of  the  Cr  ions. 

Similarly  manganese,  when  it  functions  as  a  base  with  the 
formation  of  manganous  salts,  MnCl2,  MnSC>4,  etc.,  produces 
very  pale  pink  or  nearly  colorless  solutions,  while  KMnC>4 
solutions  are  highly  colored,  due  to  the  presence  of  the  MnO^ 
ions.  In  its  salts  manganese  has  a  valency  of  two,  while  in 
the  permanganate  compounds  its  valency  is  seven,  and  it  is 
fulfilling  the  function  of  an  acid.  Hence,  the  change  from  a 
cation  to  an  anion  consists  in  increasing  the  valency  of  the 
manganese  from  two  to  seven.  The  same  is  true  for  chro- 
mium as  illustrated  above  ;  as  in  the  cation  it  has  the  valency 
of  three,  and  in  the  anion  its  valency  is  six.  In  both  cases 
we  have  the  change  from  cation  to  anion  accompanied  by  an 
increase  in  valency,  which  process  we  call  oxidation  and  the 
reverse  process  reduction. 

So,  too,  for  iron  in  ferrous  chloride  we  have  FeCl2  ^  Fe++  • 
2  Cl~.  The  solution  is  practically  colorless,  but  when  this 
is  oxidized  we  have  a  yellow  solution,  FeCl3  ^  Fe+++  •  3  Cl~, 
the  difference  being  that  in  one  case  the  colorless  ion  of  iron 
carries  two  charges,  and  the  colored  iron  ion  carries  three 
charges  of  electricity.  Hence,  the  process  of  oxidation  is 
due  to  the  increase  in  the  valency  of  the  iron  obtained  by 
adding  an  additional  faraday  of  electricity  to  the  gram-equiv- 
alent of  the  iron  ions.  It  is  evident  that  our  processes  of 
oxidation  and  reduction  may  be  explained  upon  this  basis. 

That  the  rise  in  temperature  decreases  the  degree  of  disso- 
ciation may  be  illustrated  in  the  case  of  colored  solutions. 


! 

334  PHYSICAL   CHEMISTRY 

Copper  chloride  solutions  are  blue,  and  anhydrous  copper 
chloride  is  yellow.  When  this  latter  is  added  to  aqueous 
solutions  of  copper  chloride  to  produce  concentrated  solu- 
tions, we  have  the  combination  of  the  blue  and  yellow  pro- 
ducing a  solution  with  a  decided  green  color.  If  water  is 
now  added,  the  solution  becomes  blue,  and  on  heating  the 
green  color  can  be  restored,  thus  showing  the  reduction  in 
dissociation  on  heating  the  same  as  on  increasing  the  con- 
centration of  the  solution. 

Other  properties  of  solutions,  such  as  viscosity,  surface  ten- 
sion, optical  rotatory  power,  etc.,  illustrate  the  additive 
properties  of  the  solutions  which  are  attributed  to  the  additive 
properties  of  the  dissociated  parts. 

4.  Substitution.     We  have  seen  the  effect  of  the  substitu- 
tion of  a  group  such  as  CH3  upon  the  various  properties  of 
the  compound,  such  as  boiling  point,  refraction,  etc.     The 
effect  of  the  first  substitution  is   greatest   and   diminishes 
with  the  successive  substitutions.     In  the  case  of  the  elec- 
trical conductance  of  aqueous  solutions  of  these  substitution 
products  we  likewise  find  a  marked  effect  resulting  from  these 
substitutions.     This  will  be  considered  more  in  detail  under 
the  discussion  of  the  dissociation  constant,  page  340. 

5.  The  mutual  reaction  of  two  electrolytes  resulting  in  the 
so-called  process  of  double  decomposition  is  explained  upon 
the  basis  of  the  electrolytic  dissociation  theory.     In  the  equi- 
librium equation  Ag+  -  NCV  +  H+  •  Cl-  ^±  AgCl  +  H+  •  NO3- 
expressed  as  an  ionic  reaction,  we  see  that  there  has  been 
a  disappearance  of  the  Ag  and  Cl  ions,  resulting  in  the  forma- 
tion of  AgCl,  which  we  recall  is  insoluble  and  is  precipitated. 
We  say  that  the  chlorine  and  silver  ions  cannot  exist  in  solu- 
tion at  the  same  time  and  are  consequently  precipitated.     In 
the  reaction  representing  the  neutralization  of  a  base  by  an 
acid,  we  have  Na+  •  OH~  +  H+  •  Cl-  ^±  Na+  •  Cl-  +  H2O. 
Here  we  have  the  disappearance  of  the  H+  and  OH   with  the 
formation  of  H2O,  which  is  soluble,  while  the  Na+  and  Cl"  re- 


ELECTROLYTIC  DISSOCIATION  335 

main  in  solution  as  before  the  reaction,  but  we  say  we  have  a 
salt  formed,  and  this  is  dissociated,  thus  giving  us  practically 
the  Na  and  Cl  ions  as  they  originally  existed.  We  have  the 
undissociated  water  produced  by  this  process  of  neutraliza- 
tion, and  for  all  cases  we  have  approximately  the  same 
amount  of  heat  evolved  for  each  gram-molecule  of  water  pro- 
duced. In  other  words,  neutralization  consists  in  the  forma- 
tion of  water  from  the  union  of  the  H+  and  OH~.  In  like 
manner,  the  chemical  reactions  representing  double  decom- 
positions may  be  explained.  The  application  of  the  theory 
to  Qualitative  Analysis  is  evident  and  serves  as  a  basis  for  the 
presentation  of  this  subject.  Some  authors  state  that  all 
chemical  reactions  are  ionic,  and  that  it  is  only  between  the 
ions  that  reactions  occur,  whether  these  be  in  aqueous  or  non- 
aqueous  solutions  and  even  in  cases  where  no  solvent  medium 
is  employed.  These  relations  will  be  considered  somewhat 
more  in  detail  in  a  few  specific  cases  subsequently. 


CHAPTER   XXIX 

EQUILIBRIUM  BETWEEN  THE  DISSOCIATED  AND  UNDISSO- 
CIATED  PARTS  OF  AN  ELECTROLYTE  IN  SOLUTION 

ARRHENIUS  assumed  that  the  electrolyte  exists  in  solution 
as  the  active  and  the  inactive  parts,  and  that  the  active  part 
consists  of  the  ions  or  constitutes  the  parts  into  which  the 
electrolyte  is  dissociated.  As  we  have  just  seen,  it  is  to  these 
parts,  the  ions,  that  the  chemical  reactions  are  all  attributed. 
Since  there  is  an  equilibrium  always  existing  between  these 
two  parts,  Ostwald,  as  well  as  van't  Hoff,  showed  that  the 
Mass  Law  is  applicable  to  this  equilibrium  between  the  undis- 
sociated  part  of  the  electrolyte  and  the  ions  into  which  it  is 
dissociated.  Applying  the  Mass  Action  Law  to  the  equation 

NaCl  :     Na+  •  Cl~ 


wehave 


but  the  concentration  of  the  sodium  and  chlorine  ions  is  the 
same,  as  there  are  the  same  number  of  positive  ions  produced 
as  there  are  negative  ions  when  the  NaCl  is  dissociated,  hence 
[Na+]  =  [Cl~]  and  the  equation  may  be  written 


V 
Since  we  represent  the  degree  of  dissociation  by  a,  then 

a  =  the  part  or  concentration  of  the  dissociated 

parts 
and  i  —  a  =  the  part  or  concentration  of  the  undissociated 

part. 

Substituting  these  respectively  for    [Na+]  and   [NaCl]  the 
equation  becomes 

336 


EQUILIBRIUM  OF  AN   ELECTROLYTE  IN  SOLUTION      337 


k^r 

which  becomes 

k(i  -  a)V  =  a2. 

This  is  known  as  Ostwald's  Dilution  Law,  and  may  be  written 

=  V(i-a)' 

The  degree  of  dissociation  is  usually  obtained  by  the  elec- 
trical conductance  method,  i.e.  a  =  —2-,  and  substituting  this 
value  for  a  we  have  °° 


k  = 


171  «* 

V  i  -  — 


or 


A,2 


-AV)AC 


from  which  the  value  of  k,  the  dissociation  constant,  can  be 
readily  determined  by  measuring  the  electrical  conductance, 
Ar,  at  the  volume,  V,  and  knowing  A^ .  This  Law  of  Dilu- 
tion has  been  verified  in  the  case  of  over  two  hundred  forty 
organic  acids,  and  Ostwald's  data  given  in  Table  LV  illus- 
trate the  satisfactory  agreement  for  the  values  of  k  over  a 
wide  range  of  concentration. 

TABLE  LV 


V 

ACETIC  ACID 

PROPIONIC  Aero 

SUCCINIC  Aero 

A 

ioo  a 

k 

A 

ioo  a 

k 

A 

ioo  a 

1 

8 

4-34 

I-I93 

.80  X  io~5 

3.65 

I.Ol6 

.30  X  io-5 

11.40 

3-20 

6.62  X  io'5 

16 

6.10 

I-673 

•79 

5-21 

1-452 

•34 

16.03 

4-50 

6.62 

32 

8.65 

2.38 

.82 

7.36 

2.050 

•34 

22.47 

6.32 

6.67 

64 

12.09 

3-33 

•79 

10.39 

2.895 

•35 

31-28 

8.80 

6.64 

128 

16.99 

4.68 

•79 

14.50 

4.04 

•33 

43-50 

12.24 

6.68 

256 

23-82 

6.56 

.80 

20.38 

5-68 

•33 

59.51 

16.75 

6-59 

512 

32.20 

9.14 

.80 

28.21 

7.86 

•3i 

81.64 

22.95 

6.68 

1024 

46.00 

12.66 

•77 

38.73 

10.79 

.28 

109.5 

30.82 

6.71 

A^  =  364 

309 

355 

Mean 

value         &  =  i.8oXio~B 

k  =   1.34   X   10-5 

k  =  6.65  X  io-6 

338 


PHYSICAL   CHEMISTRY 


In  Table  LV  V  is  the  volume  in  liters  of  solution  in  which 
one  gram-equivalent  of  the  acid  is  contained ;  A  the  equiva- 
lent conductance  for  the  given  volume  at  25°  C. ;  the  third 
column,  100  times  a,  the  per  cent  dissociation,  and  in  the  last 
column,  k,  the  dissociation  constant. 

Bredig  found  upon  investigation  50  bases  conforming  fairly 
well  to  the  Dilution  Law  of  Ostwald  as  the  data  in  Table  LVI 
illustrate.  The  molecular  conductance  /u.  is  expressed  in  re- 
ciprocal Siemens  units.  One  ohm  equals  i  .063  Siemens  units. 

TABLE  LVI 


AMMONIUM  HYDROXIDE 

ETHYLAMINE 

M  ETHYLAMINE 

V 

p 

looa 

i 

M 

IOOa 

i 

M 

100  a 

i 

8 

3-20 

1-35 

2.3  X  io-5 

13-8 

6-45 

5.6  X  io-4 

I4.I 

6.27 

5-2  X  io-< 

16 

4.45 

1.88 

2.3 

19.  6 

9.16 

5-8 

19.6 

8.71 

5-2 

32 

6.28 

2.65 

2-3 

27.0 

12.6 

5-7 

27.0 

12.0 

5.1 

64 

8.90 

3.76 

2.3 

36.6 

17.1 

5-5 

36.7 

I6.3 

5-o 

128 

12.63 

5-33 

2.3 

49-4 

23-1 

5-4 

49-5 

22.0 

4-9 

256 

17.88 

7-54 

2.4 

65.6 

30.7 

5-3 

654 

29.1 

4-7 

Moo  =   237 

Moo  =  214 

Moo  =   225 

Mean  k  =  2.3  X  io~5 

Mean  k  =  5.6  X  io~* 

Mean  k  =  5.0  X  io-4 

The  degree  of  dissociation  of  these  organic  acids  is  very 
slight,  and  the  same  is  true  of  the  bases  all  of  which  come 
under  the  classification  of  weak  electrolytes.  For  this  class 
of  electrolytes  the  law  was  found  to  hold  very  well.  In  the 
case  of  highly  dissociated  substances,  the  strong  electrolytes, 
no  such  uniform  values  for  the  constant  were  obtained,  and 
no  explanation  has  yet  been  given  to  account  for  this  fact. 
Many  efforts  have  been  made  to  modify  the  equation  so  that 
it  would  give  a  value  for  k  which  was  more  nearly  a  constant. 
Rudolphi  proposed  that  the  square  root  of  the  volume  be 
substituted  for  V.  The  equation  takes  the  form 


EQUILIBRIUM  OF  AN  ELECTROLYTE  IN  SOLUTION      339 


Ostwald's  equation  may  be  written  *-*r  =  k,  in  which    [i] 

\1A>\ 

is  the  concentration  of  each  of  the  ions  and  [u]  is  the  concen- 
tration of  the  un-ionized  part.  Van't  Hoff  proposed  the 
empirical  equation 

i  a 3  a1-5 

k  = — — :  or  k  = — 

(i  —  a)2V  (i  — a)  ^V 

which  then  becomes  k  =  yL- ,  which  gives  us  a  simple  relation 

between  the  concentration  of  the  ionized  parts  and  the  undis- 
sociated  part.  For  Ostwald's  formula  the  exponential  value 
is  2,  that  of  van't  Hoff  1.5,  and  Bancroft  proposed  that  the 
general  character  n  be  employed,  which  gives  the  equation 

k  =  -J^L .     He  found  that  for  strong  electrolytes  this  value 

ranges  from  1.43  to  1.56,  while  for  the  weak  electrolytes  it 
is  practically  two.  In  Table  LVII  are  given  the  values  of 
k  for  NH4C1  at  18°  C.  as  determined  by  all  three  of  these  equa- 
tions. 

TABLE   LVII 


a2        _t 

at 

*i 

V 

A 

a 

(l-a) 

(l-a)F 
Ostwald 

(i  —  a)VF 
Rudolphi 

(l-a)VP 
van't  Hoff 

I 

97.0 

•749 

.251 

2.23 

2.24 

2.58 

2 

IOI.4 

.783 

.217 

1.41 

2.OO 

2.26 

5 

106.5 

.823 

.177 

.764 

•71 

1.89 

10 

II0.7 

•855 

•145 

•504 

•59 

1.72 

20 

II5.2 

.890 

.110 

.360 

.61 

I.7I 

50 

II9.6 

.924 

.076 

.I78 

•59 

1.64 

100 

122.  1 

.942 

.058 

.122 

•53 

1-58 

2OO 

124.2 

•959 

.041 

.112 

•59 

1.62 

500 

126.2 

•975 

.025 

.076 

.70 

1.72 

IOOO 

127.3 

•983 

.017 

•057 

.80 

1.81 

5000 

128.8 

•995 

.005 

•039 

2.80 

2.80 

IOOOO 

129.2 

.998 

.002 

•005 

4.98 

4-99 

Aoo 

129-5 

340  PHYSICAL   CHEMISTRY 

Both  the  Rudolph!  and  van't  Hoff  equations  give  equally 
constant  values  for  k,  particularly  for  the  more  dilute  solutions 
(from  V  =  10  to  V  =  i ooo  liters),  while  the  Ostwald  equation 
gives  values  for  k  which  decrease  regularly  and  rapidly. 

Several  attempts  have  been  made  to  obtain  a  physical 
significance  for  van't  Kofi's  equation,  such  as  the  equations 
of  Kohlrausch,  of  Kendall,  and  of  Partington  particularly, 
whose  equation  gives  a  constant  that  passes  through  a  maxi- 
mum and  holds  only  fairly  well  for  strong  electrolytes.  It  is, 
however,  still  a  question  whether  the  Law  of  Mass  Action  can 
be  applied  to  the  electrolytic  dissociation  of  strong  electrolytes. 

Dissociation  or  lonization  Constant.  —  The  strong  elec- 
trolytes, which  include  practically  all  of  the  ordinary  inor- 
ganic acids,  bases,  and  salts,  with  a  few  exceptions,  are 
highly  dissociated,  and  the  values  of  the  dissociation  constant, 
as  we  saw  in  the  case  of  NH4C1,  are  not  of  the  same  magnitude 
for  the  different  dilutions.  But  in  the  case  of  the  weak  elec- 
trolytes, which  include  a  few  inorganic  acids,  bases,  and  salts, 
and  most  of  the  organic  acids  and  bases,  we  have  a  class  of 
substances  slightly  dissociated  to  which  the  Law  of  Mass 
Action  appears  to  be  applicable  or  sufficiently  so  that  the 
degree  of  dissociation  can  be  calculated  and  also  the  dissocia- 
tion constant.  It  is  to  be  remembered  that  the  value  of  a, 
which  as  we  have  seen  can  be  ascertained  in  a  variety  of  ways, 
is  usually  very  small.  Then  too  the  value  of  the  conductance 
at  infinite  dilution,  A^,  is  not  easy  to  determine,  and  slight 
variations  in  this  value  may  affect  the  value  of  a  greatly, 

since  — —  =a,  and  then  the  value  of  the  dissociation  constant 

A00 

becomes  somewhat  uncertain. 

There  have  been  compiled  in  Landolt-Bornstein's  Tdbellen 
the  dissociation  constants  of  a  large  number  of  acids  and 
bases,  both  inorganic  and  organic,  and  in  Table  LVIII  we 
have  selected  a  few  of  these  in  order  to  show  the  order  of  the 
constant  at  25°  C. 


EQUILIBRIUM  OF  AN   ELECTROLYTE  IN  SOLUTION      341 


TABLE  LVIII 


SUBSTANCE 

FORMULA 

VOLUME  IN  LITERS 

DISSOCIATION 
CONSTANT 

Acids 

i.  Acetic  acid     .... 

CHaCHOO 

8  —  1024 

i.  80  X  io-5 

2.  Boric  acid      .... 

BOsHs 

46  -  185 

6.6    X  10-10 

3.  Benzoic  acid  .... 

CeHsCOOH 

64  —  1024 

6.0    X  io~5 

4.  Carbonic  acid 

H2COs 

1.3    X  lo"11 

-  5.  Monochlor  acetic  aciJ 

CH2C1COOH 

16  —  1024 

1.55  X  1C-3 

6.  Dichlor  acetic  acid 

CHCUCOOH 

32  —  1024 

5.1    X  io-2 

7.  Trichlor  acetic  acid     . 

CCUCOOH 

8  -  ion  (18°  C.) 

3.0    X  iQ"1 

8.  Cyan  acetic  acid     .     . 

CH2(CN)COOH 

16  —  1024 

3-7      X  10-3 

Q.  w-chlor  benzoic  acid 

wC6H4ClCOOH 

256  —  1024 

i.  55  X  ID-" 

10.  Formic  acid  .... 

HCOOH 

8  —  1024 

2.14  X  io-< 

ii.  Hydrocyanic  acid   .     . 

HCN 

20 

7.2    X  lo"10 

12.  Hydrogen  sulphide 

H2S 

25  -  125    (18°  C.) 

5-7      XlO-8 

13.  Lactic  acid     .... 

CHsCHOHCOOH 

8  —  1024 

1.38  X  ID-" 

14.  Malonic  acid      .     .     . 

COOHCH2COOH 

1  6  —  2048 

1.58  X  I0-3 

15.  Nitrous  acid  .... 

HNO2 

512  -  1536 

4-5    Xio-< 

1  6.  Oxalic  acid     .... 

(COOH)2 

32  -  4096 

3-8    X  10-2 

17.  Phenol       

CeHsOH 

50  —  100 

1.09  X  io-10 

1  8.  Trichlor  phenol  .     .     . 

C6H2OHCU 

256  —  1024 

i.o    X  io~« 

19.  Propionic  acid    .     .     . 

CH3CH2COOH 

16  —  1024 

1.3    X  io~6 

20.  Salicylic  acid 

C6H4OH(COOH) 

64  —  1024 

1.  06  X  10-3 

21.  Succinic  acid 

C2H4(COOH)2 

1.3      X  IO-2 

22.  Sulphuric  acid    . 

H2S04 

10  —  40 

3.0      X  10-2 

23.  Tartaric  acid      .     .     . 

CH(OH)-COOH 

1  6  —  2048 

9.7    X  io~4 

I 

CH(OH)-COOH 

Bases 

i    Acetamid 

CH3CONH2 

IOO 

3.1    X  io~15 

2.  Acetanilid      .  '  .     .     . 

CHsCONHCeHs 

10               (40°  C.) 

4.1    X  io~14 

3    Ammonia 

NH3    (NH4OH) 

2   —   IOO 

1.8    X  io~5 

4.  Aniline 

C6H5NH2 

4.6    X  io~10 

5.  Cocain  . 

A  7      X  IO~7 

6.  Ethylamine    .... 

C2H6NH2 

8  -  256 

*\'  1          /^    A^ 

5-6    X  io-< 

7.  Diethylamine 

NH(C2H5)2 

8  -  256 

1.26  X  io~3 

8.  Triethylamine    .     .     . 

N(C2H5)3 

8  -  256 

6.4    X  io~4 

9.  Hydrazine      .... 

N2H6OH 

8  -  256 

3.0    X  io-« 

14.  Pyridine    

C5H5N 

50  -  599 

2.3    X  io-9 

10.  Methylamine      .     .     . 

CH3NH2 

8  -  256 

5.0    X  io~4 

ii.  Dimethylamine       .     . 

NH(CH3)2 

8  -  256 

7-4    X  io-4 

12.  Trimethylamine      .     . 

N(CH3)s 

8  -  256 

7-4    X  io-5 

13.  Butyro  nitrile     . 

C3H7CN 

IOO 

1.8    X  io-1 

15.  Urea 

CO(NH2)2 

C 

1.5    X  iQ"1 

1  6.  Strychnine     .... 

C2,H22N204 

O 

20 

1.43  X  io~7 

342  PHYSICAL   CHEMISTRY 

The  degree  of  dissociation  of  weak  acids  is  comparatively 
small,  and  a  is  therefore  very  small  as  compared  to  unity. 

Hence  in  the  equation  k  =       a  —  -  —  the  expression  (i  —  a) 

(i  -  a)  V 

is  not  materially  different  from  unity  (i),  and  the  equation 
then  becomes  k  =  ^  or  a2  =  kV,  and  a  =   V&F.     The  de- 

gree of  dissociation  of  two  acids  can  then  be  readily  compared 
by  expressing  the  ratio  of  these  two  factors  or  the  square 

root  of  the  value  of  the  dissociation  constant,  thus  —  = 

_  Oi2 


—  —  ,  and  for  the  same  volume  we  have  —  =  \^.     Since 
AjjV  <**       ^2 

the  strength  of.  acids  is  proportional  to  their  degree  of  disso- 
ciation, we  can  readily  ascertain  from  the  dissociation  con- 
stants the  relative  strength  of  the  acids  (and  the  bases  as 
well)  since  the  dissociation  constant  is  also  a  measure  of  the 
concentration  of  the  hydrogen  ions.  For  example,  from 
Table  LVI  we  find  the  dissociation  constant  for  acetic  acid 
is  1.8  X  io~5,  and  for  the  trichlor  acetic  acid  is  3.0  X  lo"1; 
we  then  have 


9fl  =  \ r'^  X  io  5  =     /o. oooo  1 8  _     /_ 

/v«  *  -?    o    N/    T  f\~  1  '  r\   t  »  i 


«2  *3.0   X    IO"1  V  0-3  ^16666.66  I2Q.I 

The  substitution  of  chlorine  for  the  hydrogen  of  the  methyl 
group  increases  the  strength  of  the  acid  enormously.  The 
same  is  true  in  the  case  of  the  bases  ammonia  and  diethyl- 
amine.  The  dissociation  constants  are  respectively  1.8  X 
i o~5  and  i. 2 6  X  io~3.  The  ratio  becomes 


01  _  ... /o. oooo  1 8  _     /_£_  = 

>'v«  *     r\    r\r\  T  i  f\  »^r/^ 


O.OOI26  ^7O          8-37 

which  shows  that  the  strength  of  the  base  is  increased  several 
times  by  substituting  two  ethyl  groups  in  place  of  the  hy- 
drogen of  ammonia. 


EQUILIBRIUM  OF  AN  ELECTROLYTE  IN  SOLUTION      343 

Isohydric  Solutions.  —  Arrhenius  showed  that  two  acids 
which  have  the  same  concentration  of  hydrogen  ions  can  be 
mixed  in  any  proportions  without  changing  their  degrees 
of  dissociation.  He  termed  these  solutions  which  have  the 
same  concentration  of  hydrogen  ions,  isokydric  solutions, 
and  went  further  and  stated,  "  what  has  just  been  said  about 
isohydric  solutions  of  acids  can  be  applied  without  change  to 
other  isohydric  solutions  which  have  a  common  ion."  Ar- 
rhenius based  this  upon  the  assumption  ^Jiat  all  electrolytes 
follow  the  dilution  law,  but  this  statement  is  too  sweeping 
and  must  be  revised  if  what  we  have  seen  above  is  true.  He 
found  that  in  the  cases  of  mixtures  of  hydrochloric  acid  and 
of  acetic  acid  the  specific  conductance  of  the  mixture  was 
practically  the  same  as  the  sum  of  the  specific  conduct- 
ances of  the  two  solutions  and  complied  with  the  mixture 
law  which  may  be  expressed  as  follows : 

V,       i  .       V. 

•v.+  vj  >va+vt 

In  this  equation  Km  is  the  specific  conductance  of  the  mix- 
ture, KO  is  the  specific  conductance  of  one  solution  at  volume 
Va,  and  Kb  is  the  specific  conductance  of  the  other  solution 
at  volume  Vb.  It  is  further  assumed  that  the  two  solutions 
are  sufficiently  dilute  so  that  the  final  volume  is  the  sum  of 
the  original  volumes,  that  is,  Va  +  Vh.  This  is  the  case 
in  concentrations  of  above  10,000  liters.  The  degree  of 
dissociation  of  weak  electrolytes  at  these  dilutions  is  very 
small,  while  that  of  the  strong  electrolytes  is  over  80  per 
cent. 

The  following  presentation  follows  Bancroft  very  closely : 
In  the  case  of  mixtures  of  solutions  of  acetic  acid  and  of 
potassium  acetate  we  have 

CHsCOOH  ^±  CH3COO-  •  H+ 
and  CH3COOK  5*  CH3COO-  •  K+ 


344  PHYSICAL  CHEMISTRY 

Assuming  the  Law  of  Mass  Action  to  hold  if  one  formula 
weight  of  acetic  acid  is  used,  then  there  will  be  formed  x 
formula  weights  of  CH3COO~  and  we  have 

7     I  —  X  _    X         X 

V     =F  '  V' 

We  have  a  different  dissociation  constant  k2  for  potassium 
acetate  than  for  acetic  acid,  as  they  are  very  differently 
dissociated,  and  we  cannot  therefore  start  with  equivalent 
quantities  in  equaf  volumes  in  order  to  obtain  the  same  con- 
centration of  the  common  anion  of  acetic  acid,  CH3COO~, 
but  with  some  concentration  such  as  C  formula  weights. 
The  Mass  Law  Equation  for  potassium  acetate  then  takes  the 

s~+ 

form  fe2     ~  *  =  —  •  —  .     Substituting    for    the    right-hand 
member  of  this  equation  its  equal  in  the  above  equation,  for 
acetic  acid  we  have  k2  —  ^-^  =  ki  '*  ~  x'  . 
Solving  for  C,  we  have 

r  _  ^1  +  fe  ~  fei)* 


Now  let  us  add  the  volume  nV  of  the  potassium  acetate 
solution  to  the  acetic  acid  solution.     We  have  for  the  acetic 

acid  i  -x         (n  +  i)x          _x 

' 


and  for  the  potassium  acetate 

^  n(C  —  x)  _  (n  -j-  i)x    ^  _     nx 


as  when  the  volume  nV  of  potassium  acetate  is  added  the 
total  volume  becomes  V  +  nV  or  (n  +  i)F,  and  the  mass 
of  the  anion  of  acetic  acid  becomes  (n  +  i)x,  and  that  of  the 
hydrogen  ion  remains  the  same,  while  the  mass  of  the  K+  is 
nx.  By  canceling  (n  +  i)  and  n,  the  equations  simplify  to 


EQUILIBRIUM  OF  AN  ELECTROLYTE  IN  SOLUTION      345 

C  '  —  X          X          X 


which  are  the  original  equations  of  equilibrium,  thus  showing 
that  the  degree  of  dissociation  of  each  of  the  electrolytes 
remains  unchanged. 

For  solutions  of  acetic  acid  and  of  zinc  acetate  we 
have  CH3COOH  ^±  CH3COO-  •  H+  and  (CH3COO)2Zn  ^± 
2  CH3COO~  •  Zn++,  from  which  we  have  respectively 


From  this  the  value  of  C  becomes 
r  _  (ki 

o   —  - 


Now  add  volume,  n  V,  of  zinc  acetate  solution  to  the  acetic 
acid  solution.     We  obtain  for  the  acetic  acid 


and  for  the  zinc  acetate 

r  n(C  —  1/2  x)  _  f(nj-i)x\2        1/2  nx 

Kz  — : . 


f(n  +  i)*V     _J 
\(n  +  i)V)       (n 


By  canceling  (n  -\-  i)  and  n  the  two  equations  reduce  to  the 
original  equilibrium  equations,  thus  showing  no  change  in  the 
degree  of  dissociation  when  the  isohydric  solutions  are  mixed 
in  any  volume. 

For  solutions  of  zinc  acetate  and  of  zinc  sulphate  we  have 

(CH3COO)2Zn  ^±  2  CH3COO-  •  Zn++ 
and  ZnSO4  ^  Zn++  •  SO4~ 

for  which  we  have,  assuming  x  formula  weights  of  zinc  ions, 
the  Mass  Law  Equations 

—  x        2  x\2      x  i   C  —  x       x       x 

—  "v'v' 


346  PHYSICAL  CHEMISTRY 

Now  add  the  volume,  nV,  of  the  zinc  acetate  solution, 
when  we  obtain  for  the  zinc  acetate 

,    n(i  -x)  _(     n2x     V      (n  +  i)* 
l(n  +  *)V     \(n+i)Vj       (n+i)V 
and  for  the  zinc  sulphate 

k    (C  ~  *)    =  (n  +  *)*    .          °° 
2(n-r-i)F      (n  -f-  i)V     (n  +  i)V 

Simplifying,  we  have 

k  d-*)  _  _*_(L*\*  .  £ 
~V~    ~n+i(v)      V 

and  fe2^*=£.|       . 

from  which  it  appears  that  for  the  zinc  sulphate  we  have  the 
same  equilibrium  equation  as  before  mixing,  but  in  the  case 

of  the  zinc  acetate  the  factor  — - —   does  not  cancel  out. 

n  +  i 

There  will  therefore  be  increased  dissociation  of  zinc  acetate, 
and  as  a  secondary  phenomenon  a  decrease  in  the  dissocia- 
tion of  zinc  sulphate. 

These  are,  however,  not  binary  electrolytes  which  Arrhe- 
nius  was  considering  in  his  generalizations.  Sodium  sulphate 
and  zinc  sulphate  are  similar  to  zinc  acetate  and  zinc  sulphate, 
and  sodium  sulphate  and  sodium  oxalate  are  analogous  to 
zinc  acetate  and  zinc  chloride.  In  the  case  of  sodium  sulphate 
and  sodium  oxalate  there  would,  however,  be  no  change  in  dis- 
sociation, but  for  sodium  sulphate  and  potassium  sulphate  or 
zinc  chloride  and  zinc  acetate  both  salts  tend  to  dissociate  and 
a  general  expression  has  been  worked  out  for  all  of  these  cases. 

Bancroft  further  applies  van't  Hoff  's  equation  to  the  case  of 
isohydric  solutions,  and  for  hydrochloric  acid  and  potassium 
chloride  shows  that  the  degree  of  dissociation  of  each  of  the 
electrolytes  should  be  decreased.  The  recent  experimental 
work  on  the  mixtures  of  salt  solutions,  including  acids,  shows 


EQUILIBRIUM  OF  AN   ELECTROLYTE  IN   SOLUTION      347 

a  decided  change  in  the  degree  of  dissociation  of  these,  and 
since  solutions  are  considered  isohydric  on  the  basis  of  their 
conductance,  it  emphasizes  Arrhenius'  definition  of  isohydric 
solutions  that  the  ion  concentration  is  independent  of  the  con- 
centration of  the  undissociated  substances.  The  concentration 
of  the  undissociated  part  is  very  great  relatively  to  the  con- 
centration of  the  ions  in  the  case  of  the  weak  electrolytes. 
We  know  that  in  many  cases  the  concentration  of  the  ions  does 
not  remain  constant,  and  particularly  is  this  true  when  salt 
solutions  containing  a  common  ion  are  mixed,  such  as  potas- 
sium cyanide  and  silver  cyanide.  Even  when  the  solutions 
containing  different  ions  are  mixed  we  have  marked  change 
in  the  conductance,  demonstrating  the  increased  dissociation 
of  many  acids  caused  by  the  presence  of  other  electrolytes, 
producing  ions  not  common  to  the  acid. 

Mutual  Effect  of  Ions.  —  The  effect  of  mixing  solutions  of 
electrolytes  may  be  illustrated  in  the  case  of  the  addition  of 
two  acids.  Let  HAi  and  HA2  be  the  two  acids,  and  their  dis- 
sociation constants  ki  and  &2  respectively.  Let  these  acids 
be  mixed  when  c\  and  c2  represents  the  concentration  of  the 
two  acids  in  the  mixture,  and  a\  and  a^  their  degree  of  disso- 
ciation respectively.  Then  in  the  mixture  we  have 

the  concentration  of  the  H+   ions  =  a\Ci  + 
the  concentration  of  the  Ai~  ions  == 
the  concentration  of  the  A2~  ions  = 


According  to  Ostwald's  Dilution  Law  we  have  for  each  acid 

ki(i  -  ai)Ci 

kz(i  —  az)c2 
This  gives  the  relation 


which  becomes 


'••• 

348  PHYSICAL   CHEMISTRY 

Now  since,  in  the  case  of  weak  electrolytes,  the  degrees  of 

dissociation  are  very  small,  it  follows  that  -  -  -»  is  approxi- 

(i  -  at) 

mately  unity,  and  the  expression  becomes  —  =  —  •  . 

kz      a2 

The  ratio  of  the  dissociation  constants  is  equal  to  the  ratio 
of  the  degrees  of  dissociation,  and  we  have  seen  that  the  acids 
with  the  greater  dissociation  constants  are  the  more  highly 
dissociated  acids  and  therefore  the  stronger. 

Let  us  consider  the  case  of  a  weak  acid,  such  as  acetic,  and 
a  strong  acid,  such  as  hydrochloric. 

For  acetic  acid  we  have  in  the  mixture  of  the  two 


and  for  hydrochloric  acid 


These  may  then  be  written  in  the  following  form  : 

ki  =  —  —  —  (aid  +  «2c2) 
i  —  «i 

and  k2  =  —  —  —  (aid  +  a2c2). 

i  —  a2 

But  in  the  case  of  acetic  acid  the  degree  of  dissociation  is  so 
slight  that  the  value  of  (i  —  cti)  is  so  nearly  unity  (i)  that 
no  great  error  will  be  made  by  this  substitution  and  our 
equation  then  takes  the  form 


In  the  case  of  dilute  solutions  of  hydrochloric  acid  the  dis- 
sociation is  practically  complete,  hence  «2  =  i.  We  then 
have  ki  =  aizci  +  a\cz.  As  a  \  is  very  small,  much  less  than 
unity,  the  value  of  the  first  term  may  be  neglected  in  com- 
parison to  the  second,  and  we  then  have  ki  =  ctiCz,  from  which 

we  have  a\  =  —  .     That  is,  the  degree  of  dissociation  of  the 


EQUILIBRIUM  OF  AN  ELECTROLYTE  IN  SOLUTION      349 

weak  acid  in  the  mixture  is  inversely  proportional  to  the  con- 
centration of  the  strong  acid.  Hence  by  adding  large  quan- 
tities of  hydrochloric  acid  to  an  acetic  acid  solution,  the 
dissociation  of  the  acetic  acid  will  be  forced  back  and  may 
become  practically  undissociated. 

The  forcing  back  of  the  dissociation  is  of  great  importance 
in  analytical  chemistry,  as  may  be  illustrated  in  a  large  num- 
ber of  cases.  When  NH4OH  is  added  to  a  solution  of  MgCl2, 
a  precipitate  of  Mg(OH)2  is  produced  according  to  the  ionic 
reaction, 

Mg++  •  2  Cl-  +  2  NH4+  •  OH-  ^±  Mg(OH)2  +  2  NH4+  •  CK 

Now  NH4OH  is  a  weak  base  and  therefore  produces  few 
OH  ions,  according  to  the  ionic  equilibrium  equation  NH4OH 
^±  NH4+  •  OH~ ,  for  which  we  would  have  the  Mass  Law 

Equation         k  [NH4OH]  = 
V 

Now  when  mixed  with  a  strong  electrolyte  containing  the 
common  NH4  ion,  such  as  any  ammonium  salt,  the  concen- 
tration of  the  ions  furnished  by  this  would  be  very  much  in 
excess  of  that  furnished  by  the  NH4OH.  According  to  the 
equilibrium  equation  above  we  readily  see  that  with  the 
increase  of  the  concentration  of  the  NHiCl  the  value  for 
the  degree  of  dissociation  of  the  NH4OH  becomes  very  small 
and  can  be  decreased  to  such  an  extent  that  the  number  re- 
quired for  the  formation  of  Mg(OH)2  is  not  sufficient  to  pro- 
duce enough  of  the  Mg(OH)2  to  precipitate ;  i.e.  it  will  all 
remain  in  solution.  So  in  the  preparation  of  the  so-called 
magnesium  mixture  enough  ammonium  salts  are  added  to 
prevent  the  ionization  of  the  NH4OH  to  the  extent  necessary 
to  produce  enough  Mg(OH)2  so  that  it  will  exceed  its  solu- 
bility. Since  the  hydroxides  of  Fe,  Al,  and  Zn  are  but 
slightly  soluble,  it  is  more  difficult  to  prevent  their  precipita- 
tion in  this  manner. 


350  PHYSICAL   CHEMISTRY 

Ionic  Product.  —  If  the  dissociation  of  the  precipitating 
reagent  can  be  forced  back  to  such  an  extent  that  the  ions 
it  produces  are  practically  negligible,  then  to  precipitate  a 
substance  and  prevent  it  from  going  into  solution  again  would 
require  the  presence  of  a  large  number  of  either  of  the  ions 
resulting  from  the  solution  of  that  substance.  For  example, 
if  to  a  solution  of  BaCl2  a  concentrated  solution  of  HC1  be 
added,  the  concentration  of  the  chlorine  ion  can  be  increased 
to  such  an  extent  that  the  BaCl2  will  be  precipitated.  For 
this  reason  it  is  recommended  that  an  excess  of  the  precipi- 
tating reagent  be  added. 

In  order  to  prevent  the  precipitate  from  redissolving, 
the  precipitating  reagent  containing  an  ion  in  common  with 
the  saturated  solution  is  present  in  excess,  but  as  the  precipi- 
tate is  washed  and  thus  separated  from  the  excess  of  the 
common  ion,  the  pure  water  will  dissolve  the  precipitate. 
It  is  therefore  necessary  to  wash  the  precipitate  with  wash 
water  which  contains  an  ion  common  with  that  produced 
in  saturated  solutions  of  the  precipitate.  Magnesium  am- 
monium phosphate  is  washed  with  ammonia  water,  am- 
monium phosphomolybdate  with  a  solution  of  NH4NO3, 
PbS04  with  wash  water  cpntaining  H2SO4,  etc.  Electrolytes 
chosen  for  this  purpose  should  be  readily  volatile  if  the  pre- 
cipitate is  to  be  weighed. 

In  saturated  solutions  the  concentration  of  the  undisso- 
ciated  solute  in  solution  is  in  equilibrium  with  the  solid 
solute,  and  this  concentration  is  a  constant  quantity.  The 
solute  in  solution  is  dissociated  and  there  exists,  as  we  have 
seen,  a  condition  which  is  represented  by  the  equilibrium  re- 
lation AgC1  ^  AgC1  _>  Ag+  ,  Q_ 

solid  undis- 

sociated 

and  for  a  saturated  solution  the  concentration  of  the  undis- 
sociated  solute  is  a  constant.  It  is  evident  that  the  silver  ion 
and  the  chlorine  ion  are  found  in  equivalent  quantities  and  in 


EQUILIBRIUM  OF  AN   ELECTROLYTE  IN   SOLUTION      351 

definite  concentrations,  and  according  to  the  Law  of  Mass 
Action  we  have  the  products  of  the  concentration  of  the  ions 
proportional  to  the  concentration  of  the  undissociated  part, 
and  as  this  latter  is  constant  we  then  have  [Ag+]  •  [Cl~]  = 
a  constant,  which  is  usually  designated  by  L0  and  is  called  the 
Solubility  Product  or  the  Ionic  Product.  This  equation  is  then 

Lo  =  [Ag+J  •  [Cl-]. 

Lewis  says,  "  Again,  as  already  pointed  out,  the  saturated 
solution  of  a  body  such  as  AgCl  is  very  dilute,  and  since  it 
is  a  salt,  the  small  quantity  which  is  dissolved  suffers  almost 
complete  dissociation  in  solution.  Hence  the  concentration 
of  the  undissociated  molecules  must  be  small  compared  even 
with  the  ions.  That  is,  CQ  is  negligible  compared  to  the  con- 
centration [Ag+]  or  [Cl~].  Hence  in  such  a  case,  say  when 
AgCl  is  dissolved  in  water  alone,  the  concentration  of  Ag+  or 
Cl~  in  gram  ions  per  liter  gives  a  number  identical  with  the 
solubility  of  the  entire  salt.  But  [Ag+]  •  [Cl~]  =  LO.  Hence 
the  solubility  is  identical  with  the  V  solubility  product.  Now 
take  the  case  of  AgCl  in  presence  of  some  KC1.  The  solu- 
bility simply  becomes  identical  with  the  concentration  of  the 
least  represented  ion,  i.e.  the  Ag+  ion.  An  estimation  of  the 
Ag+  ion  in  solution  is  therefore  the  experimental  way  of  ar- 
riving at  the  solubility  of  AgCl  in  aqueous  KC1  solution.  We 
can  evidently  calculate  this  quantity  if  we  know  what  value 
Lo  has  (say  by  estimating  the  Ag+  or  Cl~  in  absence  of  KC1) 
and  remembering  that  Lo  is  constant  whether  KC1  is  present 
or  not.  By  the  addition  of  KC1  in  a  given  amount  we  know 
the  quantity  of  Cl~  present  (the  Cl~  originally  present  from 
the  AgCl  itself  being  usually  negligible  compared  to  the 
quantity  added),  and  the  '  solubility  '  of  the  AgCl  in  pres- 
ence of  KC1,  or  the  Ag+  concentration  is  simply 


[C1 


352  PHYSICAL   CHEMISTRY 

The  numerical  value  of  the  ionic  product  may  be  calculated 
if  the  solubility  of  the  salt  and  its  degree  of  dissociation  are 
known.  At  25°  the  solubility  of  BaSO4  is  0.0023  gram  per 
liter,  or  practically  o.o4i  mole.  The  BaSO4  is  assumed  to 
be  completely  dissociated,  then  Lo  =  [Ba++]  •  [SO4~]  = 
o.o4i  X  0.041  =  o.ogi,  which  is  the  ionic  product  of  BaSO4, 
and  as  determined  by  Hulett  is  0.94  X  io~10.  The  amount 
of  BaSO4  remaining  in  solution  would  be  very  small,  23  mg. 
per  liter.  In  the  determination  of  sulphur  in  sulphates  by  the 
BaQ2  method  the  SO4  ions  left  would  be  reduced  by  a  slight 
excess  of  BaCl2  so  that  there  would  be  but  a  small  fraction  of 
a  milligram  per  liter  remaining.  We  have  again  emphasized 
the  necessity  for  adding  a  small  excess  of  the  precipitating 
reagent. 

The  ionic  product  of  Agl  is  much  smaller  than  that  of  AgCl, 
so  that  on  the  addition  of  a  solution  of  KI  to  a  saturated  solu- 
tion of  AgCl  in  equilibrium  with  an  excess  of  the  solid  AgCl 
the  concentration  of  the  Ag+  would  be  decreased.  This  will 
result  in  a  final  state  of  equilibrium  according  to  the  following 
equation  : 


AgCl  ^±  AgCl    ^  Ag+  4-  Cl-  +  K+  +  I-  ;£    Agl    ;£  Agl 

solid  undisspciated  undissociated        solid 

(negligible)  (negligible) 

solution 

When  equilibrium  is  established,  the  concentration  of  the  ions 
must  be  such  that  their  products  are  the  ionic  products 
(solubility  products)  of  the  silver  chloride  and  of  the  silver 
iodide,  that  is,  [Ag+]  .  [C1-,  =  LAgQ 

[Ag+]  •    [I-]    = 


But  the  concentration  of  the  Ag+  is  the  same  in  both  cases, 
therefore  by  division  we  have 


[Cl-]_L 


Agci 


EQUILIBRIUM  OF  AN  ELECTROLYTE   IN   SOLUTION      353 


This  means  that  at  equilibrium  the  concentration  of  the  Cl 
must  be  greater  than  the  concentration  of  the  I~  in  the  ratio 
of  their  ionic  products.     The  ionic  product  of  AgCl  is  1.56  X 
io~10  and  of  Agl  is  0.94  X  io~16,  then 


[I-]       0.94  X  icr16 

which  means  that  the  concentration  of  the  I~  must  become 
about  one  millionth  of  that  of  the  chlorine  ions,  hence  virtu- 
ally all  of  the  AgCl  can  be  transformed  into  Agl  and  prac- 
tically all  of  the  silver  precipitated  from  the  solution. 

In  Table  LIX  there  are  compiled  the  values  of  the  Ionic 
Product  or  Solubility  Product  of  a  few  of  the  more  common 
compounds. 

TABLE  LIX  —  IONIC  PRODUCT 


SUBSTANCE 

TEMP. 

IONIC  PRODUCT 

Ks 

Silver  chloride       .... 
Silver  chromate     .... 
Silver  bromide            .     T     . 
Silver  oxalate 

25° 

25 
25 
25 
25 
25 
25 
25 

18 
18 
18 

18 
18 
25 
25 

[Ag+  •  [C1-] 
[Ag+2«  [Cr04~l 
[Ag+  •  [Br~] 
[Ag+2-  [C2Or~] 
[Ag+  -  [I-] 
[Ag+  •  [10,—] 
[Da**]  •  [S04~] 
[Ca++]  •  [C2O4~~] 
[Ca4"1-]  •  [SO4~~] 

[Pb++]  •  [C2O4—  ] 
[Pb++]  •  [CrO4—  ] 

[H+]  •  [OH-] 

1.56  X   ICTi0 

9  X  io~12 
4.4  X  icr13 
1.03  X  iQ-11 
i.i     X  io~16 
3.49  X  icr8 
0.94  X  io~10 
2.57  X  icr9 
6.1     X  icr5 
1.2    X  icr11 
1.4    X  icr15 
3-5    X  icr11 
1.77  X  icr14 
0.61  X  io~8 
2.21  X  icr4 
1.04  X  io~14 

Silver  iodide     
Silver  iodate 

Barium  sulphate  .... 
Calcium  oxalate  +  H2O 
Calcium  sulphate       .     .     . 
Magnesium  hydroxide    .     . 
Manganese  sulphide  .     .     . 
Lead  oxalate                   .     . 

Lead  chromate      .     .     .     * 
Lead  sulphate  
Thallium  chloride      .     .     . 
Water      .     .     .     .     .     .     . 

RELATIVE  STRENGTH  OF  ACIDS  AND  BASES 

The  relative  strength  of  acids  and  bases  depends  upon  the 
conditions  under  which  they  react,  or  in  other  words,  upon 


354  PHYSICAL   CHEMISTRY 

whether  the  conditions  under  which  they  react  are  such  that 
both  are  under  the  most  favorable  conditions.  If  many  acids 
or  salts  of  these  acids  are  treated  with  H2SO4  and  heated, 
sulphuric  acid  will  take  their  place,  according  to  the  reaction 
H2SO4  +  2  NaCl  =  Na2SO4  +  2  HC1,  which  is  the  usual 
method  for  the  preparation  of  HC1.  From  such  reactions 
one  would  say  that  H2SO4  is  the  stronger  acid.  If  a  number 
of  acids  or  their  salts  are  heated,  they  would  pass  off  in  the 
order  of  their  volatility,  and  phosphoric  acid  would  be  among 
the  ones  to  remain,  therefore  phosphoric  acid  would  be  con- 
sidered stronger  than  HC1  or  HNOs.  In  the  glazing  of  pot- 
tery NaCl  is  introduced  on  to  the  hot  pottery,  which  is  covered 
with  SiO2,  where  we  have  a  replacement  of  the  chlorine  with 
the  formation  of  sodium  silicate.  By  analogous  reasoning 
we  should  conclude  that  silicic  acid  is  stronger  than  hydro- 
chloric acid.  The  difficulty  with  methods  of  this  kind  is  that 
under  the  conditions  the  two  acids  have  not  equal  chances 
to  compete  for  the  base,  as  one  of  the  acids  is  volatile  and 
is  readily  removed  from  the  scene  of  action. 

Many  terms  have  been  applied  to  what  we  call  strength  of 
acids,  such  as  affinity,  activity,  and  avidity.  Many  methods 
have  been  devised  for  determining  the  strength  or  avidity 
of  acids,  such  as  the  method  of  "  turning  out  "  one  by  the 
other,  but  we  have  seen  that  this  is  not  a  really  satisfactory 
method. 

Since  the  degree  of  dissociation  determines  the  number  of 
hydrogen  ions,  and  this  is  readily  ascertained  from  the 
electrical  conductivity  method,  we  then  have  a  satisfactory 
and  convenient  method  for  ascertaining  the  relative  strength 
of  acids  from  their  conductance.  From  the  values  of  the  dis- 
sociation constants  given  in  Table  LVIII  the  relative  strength 
of  these  weak  acids  can  be  readily  obtained. 

Suppose  we  have  two  weak  acids,  HAi  and  HA2,  which 
form  salts  with  the  strong  base  BOH.  Let  us  assume  that  we 
have  one  mole  each  of  the  two  acids  and  of  the  base.  Then 


EQUILIBRIUM  OF  AN  ELECTROLYTE  IN  SOLUTION      355 

there  will  not  be  enough  of  the  base  to  supply  the  require- 
ments of  the  two  acids,  and  so  it  will  be  distributed  between 
the  acids  in  proportion  to  their  dissociation.  Let  x  be  the 
fraction  of  a  mole  which  reacts  with  the  acid  HAi,  then  (i  —  x) 
moles  of  the  base  react  with  the  acid  HA2.  Accordingly  we 
shall  then  have  the  equilibrium  equation 

BAi  +  HA2  :£  BA2  +  HAi. 

From  which  the  concentrations  are 

x  moles  of  the  salt  BAi  and  (i  —  00}  moles  of  HAi 
(i  —  x)  moles  of  the  salt  BA2  and  x  moles  of  HA2. 

Now  assuming  that  Ostwald's  Dilution  Law  holds,  we  have 
for  the  two  acids 

k    .-  [H+]  •  [Ar]  _  [H+]  .  [x] 
[HA!]  [i  -  x] 


and 


-  x 


[HA,]  [x] 

The  above  equations  then  become,  dividing  the  one  by  the 

°ther'       *i  =  [H+]  •  [x]  •  [x]          _        MI 

k,       [i  -*]  •  [H+]  •  [i  -*]       [i-*]2' 

But  since  the  distribution  of  the  base  between  the  two  acids 
is  in  the  ratio  of  their  degrees  of  dissociation,  and  when  one 
mole  of  the  base  meets  with  one  mole  each  of  the  two  acids  we 
have 


or 


_!*]_  =  J*T 

I   -  X\         \  tl 


h       [i  -  x]*          [i  -x] 

Hence,  the  distribution  ratio  is  obtained  by  determining  the 
dissociation  constant  of  each  acid  and  the  ratio  of  the  strength 
of  the  acids  is  equal  to  the  square  root  of  the  ratio  of  the  dis- 
sociation constants. 

Thomsen's  Thermochemical  method  for  the  determination 
of  the  relative  strength  of  acids,  of  their  avidity,  as  he  termed 


356 


PHYSICAL   CHEMISTRY 


it,  consisted  in  treating  a  salt  of  an  acid,  Na2SO4,  with  HC1, 
and  determining  the  heat  effect.  Having  determined  the 
heat  of  neutralization  of  NaOH  by  H2SO4  and  by  HC1,  and  the 
actual  heat  absorbed  when  Na2SO4  reacts  with  HC1,  it  would 
be  an  easy  matter  to  calculate  the  proportion  of  the  sodium 
sulphate  converted  into  sodium  chloride.  From  this  the 
relative  amounts  of  the  sodium  distributed  between  the  two 
acids  can  be  readily  ascertained. 

By  employing  this  method  Thomsen  determined  the  rela- 
tive strengths  of  a  number  of  acids  upon  the  basis  of  HC1  as 
100  and  his  values  are  given  in  Table  LX  under  the  heading 
Avidity. 

TABLE   LX  —  RELATIVE   STRENGTH   OF   ACIDS   AS   DETER- 
MINED BY  A  NUMBER  OF  THE  COMMON  METHODS, 
ASSUMING  HCL  =  100 
(After  Walker) 


VELOCITY 

CONSTANTS 

Aero 

AVIDITY 

ELECTRICAL 
CONDUCTANCE 

Sugar 
Inversion 

Catalysis 
of  Acetate 

Hydrochloric  .     .     . 
Nitric    .     .     .     »/;  ,-; 
Sulphuric  .     .     ,    . 
Oxalic    

IOO 
100 

49 
24. 

IOO 
99.6 
65.1 
10.7 

IOO 
IOO 

53 
18.6 

IOO 
91-5 

54-7 
17.4 

Ortho  phosphoric     . 
Monochloracetic 
Tartaric     .... 
Acetic    

13 
9 

5 
3 

7-3 
4-9 
2-3 
0.4 

6.2 

4.8 
0.4 

4-3 
2.3 
0-35 

A  number  of  other  methods  for  ascertaining  the  relative 
strength  of  acids  and  bases  have  been  employed,  such  as  the 
volume  method  of  Ostwald,  which  consists  in  measuring  the 
change  in  volume  produced  by  the  reaction  of  various  salts 
of  the  acids  with  the  different  acids.  From  these  volume 


EQUILIBRIUM  OF  AN  ELECTROLYTE  IN  SOLUTION      357 

changes  Ostwald  calculated  the  relative  strength  of  some 
of  the  more  common  acids  and  found  the  same  general  order 
to  prevail  as  by  the  other  methods.  The  values  as  deter- 
mined by  the  rate  of  inversion  of  cane  sugar  and  by  the 
catalysis  of  an  acetate  are  in  agreement  with  the  other 
methods.  These  two  methods  will  be  referred  to  subse- 
quently. 

The  order  is  the  same  by  all  methods. 

Practically  the  same  methods  may  be  employed  for  de- 
termining the  relative  strength  of  bases.  The  values  in 
Table  LXI  illustrate  about  the  average  relative  strength  of  the 
common  bases  and  their  order,  assuming  lithium  hydroxide 
as  100. 

TABLE   LXI 

(After  Walker) 


BASES 


Lithium  hydroxide 

Sodium  hydroxide 

Potassium  hydroxide      .     .     .     . 
Thallium  hydroxide  .     .     .     . 
Tetraethylammonium  hydroxide 
Triethylammonium  hydroxide     . 
Diethylammonium  hydroxide 
Ethylammonium  hydroxide     .     . 
Ammonium  hydroxide   . 


AVIDITY 


100 
98 
98 
89 

75 

14 

16 

12 
2 


The  hydroxides  of  the  alkalies  are  practically  completely 
dissociated  and  are  the  strong  bases,  the  hydroxides  of  the 
alkaline  earths  are  also  strong  bases,  while  ammonium  hy- 
droxide is  a  very  weak  base. 


CHAPTER   XXX 
CONCENTRATED   SOLUTIONS 

IN  the  presentation  of  the  relations  of  the  vapor  pressure 
to  osmotic  pressure  it  was  emphasized  that  The  Gas  Law  could 
be  applied  to  solutions,  but  that  these  solutions  had  to  be  of 
the  type  known  as  ideal  or  perfect  solutions,  and  this  is  analo- 
gous to  the  statement  that  The  Gas  Law  holds  only  for  Per- 
fect Gases.  We  saw  that  certain  modifications  of  The  Gas 
Law  were  made  in  attempting  to  use  it  in  connection  with 
most  gases  under  the  usual  conditions  ;  so,  too,  in  the  appli- 
cation of  The  Gas  Law  to  solutions  other  than  the  perfect 
solutions  certain  modifications  must  be  made  in  order  to  take 
into  consideration  the  numerous  assumptions  postulated  in 
connection  with  the  applications  of  The  Gas  Law. 

In  the  formulation  of  his  Modern  Theory  of  Solutions  van't 
Hoff  fully  realized  the  limitations  of  his  conceptions  of  solu- 
tions and  showed  the  necessity  of  limiting  its  application,  and 
in  his  presentation  stipulated  the  explicit  assumptions  made 
in  applying  the  Laws  of  Gases  to  solutions  ;  and  these  may  be 
summarized  as  follows : 

1 .  There  is  no  reaction  between  the  solvent  and  the  solute. 

2.  The  solvent  and  the  solute  are  neither  associated  nor 
dissociated. 

3.  The  compressibility  of  the  solution  is  negligible. 

4.  The  Heat  of  Dilution  of  the  solution  is  zero. 

We  know  from  experience,  in  many  solutions  at  least,  that 
there  is  a  marked  reaction  between  the  solvent  and  solute 
and  that  the  heat  of  dilution  is  zero  in  but  few  cases.  Further, 
we  have  just  been  considering  a  number  of  methods  by  means 

358 


CONCENTRATED  SOLUTIONS  359 

of  which  the  dissociation  of  the  solute  can  be  determined, 
and  we  have  also  presented  methods  for  determining  the 
association  constant  of  liquids.  It  will  therefore  be  neces- 
sary for  us  to  take  up  a  more  detailed  consideration  of  these 
assumptions  and  see  in  what  ways  van't  HofFs  formula  will 
be  affected  by  dropping  each  and  all  of  these  assumptions. 

Weight  Normality.  —  As  van  der  Waals'  equation  was  one 
of  the  modifications  of  the  Gas  Law  Equation  to  account 
for  the  variations  from  the  law  that  occurred  in  concentrated 
gases,  there  are  likewise  numerous  equations  which  attempt 
to  represent  the  quantitative  relations  between  the  osmotic 
pressure  and  the  concentration  of  the  solution  by  correcting 
for  the  mutual  attraction  of  the  solute  molecules  and  also  for 
the  attraction  between  the  solvent  and  solute.  The  main 
idea  is  to  get  an  expression  which  would  incorporate  the 
volume  of  the  solvent  and  not  the  volume  of  the  solution  that 
contained  the  molar  concentration  of  the  solute.  It  was 
through  the  work  of  Earl  of  Berkeley  and  E.  G.  J.  Hartley 
and  of  Morse  that  the  best  agreement  between  theory  and 
experimental  data  was  obtained  by  expressing  the  concen- 
tration in  terms  of  weight  normality  instead  of  volume  nor- 
mality, as  was  done  by  van't  Hoff,  and  is  usually  employed 
in  practically  all  lines  of  experimental  work. 

What  difference  these  methods  of  expressing  the  concen- 
tration makes  will  become  more  apparent  by  a  specific  ex- 
ample. Suppose  we  have  a  40  per  cent  cane  sugar  solution. 
What  is  the  normal  volume  concentration  of  this  solution  and 
what  is  the  normal  weight  concentration?  The  specific 
gravity  of  a  40  per  cent  sugar  solution  at  20°  C.  is  1.17648 ; 
then  one  liter  of  this  solution  would  weigh  1176.48  grams, 
and  it  would  contain  470.59  grams  or  1.376  moles  of  sugar  and 
705.89  grams  of  water.  That  is,  there  are  1.376  moles  of  sugar 
contained  in  one  liter  of  a  40  per  cent  sugar  solution.  Now 
by  weight  normal  we  mean  the  number  of  moles  contained 
in  1000  grams  of  water.  Since  there  are  470.59  grams  of 


360  PHYSICAL   CHEMISTRY 

sugar  contained  in  705.89  grams  of  water,  then  we  have 
470.59  :  705.89  ::  x:  1000  grams.  Solving  for  x,  we  have 
666.7,  therefore  there  are  666.7  grams,  or  1.9493  moles,  of 
sugar  in  i  ooo  grams  of  water.  From  this  then  we  see  that  a  40 
per  cent  sugar  solution  expressed  as  a  normal  volume  solution 
would  have  a  concentration  of  1.376  moles  dissolved  in  one 
liter  of  the  solution,  and  expressed  as  a  normal  weight  con- 
centration of  1.949  moles  dissolved  in  one  liter  of  solvent. 
So  it  is  apparent  that  there  is  a  very  decided  difference 
whether  our  concentration  is  expressed  as  a  normal  volume 
or  as  a  normal  weight  concentration.  As  stated  above, 
Morse  found  better  agreement  between  the  experimental 
results  and  theoretical  values  by  employing  normal  weight, 
that  is,  a  volume  of  1000  grams  of  the  solvent. 

Thermodynamic  Equations  for  Concentrated  Solutions.  — 
For  solutions  a  complete  thermodynamic  equation  would  be 
very  complicated,  as  it  would  have  to  take  into  considera- 
tion a  large  number  of  assumptions  concerning  the  two  com- 
ponents, the  solvent  and  the  solute.  The  expression  would 
have  to  include  among  other  assumptions  the  molecular 
state  of  the  solvent  and  of  the  solute,  their  volume  change 
when  mixed,  the  heat  of  dilution,  compressibility,  etc.  By 
simplifying  the  conditions  there  has  been  obtained  a  general 
equation  for  ideal  or  perfect  solutions  by  assuming  that  these 
two  components  do  not  interact  with  each  other,  that  there 
is  no  heat  of  dilution,  that  the  resulting  volume  on  dilution 
is  the  sum  of  the  original  volume  plus  that  of  the  solvent, 
and  that  the  properties  are  intermediate  between  the  prop- 
erties of  the  pure  components. 

Previously  we  saw  that  logfl  p/pi  = ^  and  since  —  = 

P  Rl  P 

VP 

the  molecular  volume  Vm  we  have  loge  p/pi  =  -—— ,  from  which 

K 1 

RT 

we  get  p0  =  ——-  loge  p/pi  .     From  Raoult's  Law  we  have 

*  m 


CONCENTRATED  SOLUTIONS  361 

•-.;.;.  p  —  pi  _  n 

p  N 

which  gives  us 

T  -Pl  =  JL 
p       N 

and  if  we  define  the  ratio  of  the  number  of  molecules  of  the 
solute  to  the  total  number  of  molecules  by  x,  then  %  =  —  . 

Substituting  and  transposing  we  obtain  &  =*  i  —  x.     Sub- 

P 


stituting  this  value  of  «  in  the  equation  pn  =  -  —  (  loge  •£  ) 
P  Vm\       Pi/ 

RT 
we   have  p0  =  ——  [—  log,    (i  —  x)],   which   on   expanding 

*  m 

log  (i  —  x)  into  a  series,  the  equation  then  takes  the  form 


RT 


This  equation,  into  which  a  factor  for  the  compressibility 
of  the  solutions  has  been  introduced,  is  the  one  given  by 
Findlay  and  takes  the  following  form  : 


r 


RT 


in  which  p0  is  the  osmotic  pressure  and  defined  as  the  addi- 
tional pressure  that  must  be  put  upon  the  solution  to  prevent 
the  inflow  of  the  solvent  through  a  perfectly  semipermeable 
membrane,  Vm  is  the  molecular  volume  of  the  solvent  under 
standard  pressure,  x  is  the  ratio  of  the  number  of  moles  of 
the  solute  to  the  number  of  moles  of  the  solvent,  and  a  is  the 
coefficient  of  compressibility.  But  since  the  compressibility 
of  solutions  is  very  slight  except  for  enormous  pressures,  it  is 
assumed  for  moderate  pressures  that  the  compressibility  fac- 


362  PHYSICAL  CHEMISTRY 

tor  is  negligible,  and  no  appreciable  error  is  introduced  by 
omitting  this  factor  entirely. 

So  employing  the  equation  without  the  compressibility 
factor  we  have 


For  concentrated  solutions  Raoult  used  N  +  n  as  the  total 
number  of  molecules  in  the  system  and  then  x  would  be 

—  -  —  ,  and  substituting  in  the  above  equation  this  value. 
N  +  n 

we  have  RT     n      f     .         n          . 

f 


In  the  case  of  infinitely  dilute  solutions,  however,   —  —  — 

N  +  n 

becomes  —  ,  and  the  value  of  this  fraction  becomes  very 

N 

small  and  the  terms  involving  the  higher   powers  of  the 
fraction  are  negligible.     The  equation  then  simplifies  to 

_RT  n_ 

Po~  Vn  N 
Now  since  VmN  represents  the  volume,  V,  of  the  solution  it- 

self we  have  p0=  ^-—  ,  or  pQV  =  nRT,  which  is  the  usual 

form  of  van't  Hoff  's  equation  or  the  Gas  Law  Equation. 
Another  Form  of  the   Equation.  —  By  employing  a  method  of  ex- 

.  IT)  /T-i  L 

pansion  l  for  the  term  log  •£•  in  the  equation  pn  =  —  log  -£,  different 
Pi  Vm         pi 

from  the  one  employed  above,  we  obtain  the  following  : 

l(P  ~  frV  +  ...1 
5(p  +  pJ 

From  Raoult  's  formula  -  -  —  =  —  -  —  the  following  relation  may  be 
p          N  +  n 

obtained  :  P  ~  P1  =  -  5  --    Substituting  this  value  in  the  above 
p  +  pi      2N  +  n 

equation  we  have 

1  See  Wells'  College  Algebra. 


CONCENTRATED  SOLUTIONS  363 


.         RT 

?= 


This  equation  may  preferably  be  employed  for  the  calculation  of 
the  osmotic  pressure  from  the  experimental  data.  Exact  values  are 
obtained  by  employing  the  first  term  of  this  expression,  while  with  the 
other  formula  two  and  sometimes  three  terms  are  required  for  the  same 
degree  of  exactness. 

It  will  be  recalled  that  Morse  employed  normal  weight 
concentrations  in  expressing  his  osmotic  pressure  results. 
So  in  the  equation 

_  RT       n      T     ,  n          ,  if     n      V,       "1 

'   Vm  N  +  nLI'*~2(N  +  n)^3\N  +  n)~    "J 

the  values  for  a  solution  containing  n  moles  of  sugar  dissolved 
in  1000  grams  of  water  at  20°  C.  would  be  :  T  =  273°  -+-  20°  = 
2  93°  ;  V  being  the  volume  of  1000  grams  of  water  at  20°, 
which  is  1001.8  cc.  ;  N,  the  number  of  moles  of  water,  is  1000 
-i-  1  8  =  55.5  ;  the  molecular  volume  Vm  is  1001.8  divided  by 

55.5  ;  %  =  -  -  ;  R  =  81.6  cc.  atmos.,  as  employed  by 

Morse  on  the  basis  that  H  =  i  instead  of  the  usual  value 
82.04  cc.  atmospheres. 

Substituting  these  values,  we  have 


=  81.6  X  293  X  55-5  .         n       (     ,  n  .       \ 

1001.8  55-5+  n\         2(55.5  +  »)  / 


from  which  the  osmotic  pressure  may  be  calculated.  This 
gives  us  the  osmotic  pressure  of  solutions  by  means  of  which 
Morse's  observed  values  are  checked  fairly  closely,  as  shown 
in  the  third  column  of  Table  LX. 

Now  let  us  assume  that  the  solvent  is  associated,  then  the 
equation  takes  the  form 


364  PHYSICAL   CHEMISTRY 

RT      n 


where  a  is  the  association  factor  for  the  solvent.     The  num- 

ber of  moles  of  the  solvent  then  is  — 

a 

According  to  van  Laar  the  association  factor,  a,  for  water 
at  20°  C.  is  1.65,  and  the  number  of  associated  molecules  in 


iooo  grams  of  water  is  *"1*  =  33.7,  and  the  molecular  vol- 

1.65 

ume  of  the  associated  molecule  is  I001'  ,  which  is  Vm  of  the 

33-7 

formula.  Substituting  these  values  in  the  equation  above 
and  calculating  for  the  osmotic  pressure,  we  obtain  23.5  at- 
mospheres as  against  the  value  23.64  without  correction  for 
the  association  of  the  solvent.  These  values  are  practically 
the  same,  showing  that  up  to  this  concentration  the  associa- 
tion of  the  solvent  can  be  neglected. 

Even  making  the  calculations  upon  the  basis  of  normal 
weight  relations  instead  of  normal  volume  relations,  and 
correcting  for  the  association  of  the  solvent,  there  still  remains 
some  considerable  discrepancy  between  the  experimental 
values  of  the  osmotic  pressure  and  the  values  calculated 
in  the  manner  just  indicated.  Now  let  us  make  the  addi- 
tional assumption  that  the  solvent  and  the  solute  do  react 
with  the  formation  of  hydrates  of  the  solute.  In  the  process 
of  hydration  there  is  then  removed  from  the  solvent  that 
amount  of  the  solvent  which  is  in  combination  with  the  solute 
molecules,  and  this  quantity  will  disappear  in  so  far  as  its 
action  as  a  solvent  is  concerned.  Hence  the  number  of  mole- 
cules of  solvent  will  be  decreased  by  this  amount.  Then 
the  equation  becomes 

RT  n  [     ,  n  , 

P°       Vm  N  -  (3n  +  nl         2(N  -  pn  +  n) 


CONCENTRATED   SOLUTIONS 


365 


in  which  we  have  introduced  the  correction  /3  for  the  number 
of  molecules  of  the  solvent  combining  with  each  molecule 
of  the  solute,  and  (3n  is  then  the  number  of  moles  of  solvent 
that  have  disappeared  from  the  scene  of  action  as  solvent. 
The  molecular  volume  of  the  solvent  then  should  be  the 
volume  of  (1000  —  18  (3n)  grams  of  water  at  the  specified 
temperature,  divided  by  (N  —  (3n),  the  number  of  molecules 
of  solvent  actually  serving  as  solvent.  The  values  as  calcu- 
lated according  to  this  assumption  with  /3  =  5  are  given  in 
the  fifth  column  of  Table  LXII. 

TABLE   LXII 

(Findlay's  Osmotic  Pressure,  page  41) 


OSMOTIC  PRESSURE  CALCULATED  BY  ABOVE  EQUATIONS 

WEIGHT 
NORMAL 

OSMOTIC 
PRESSURE 
OBSERVED 

Assuming   no 
Hydration  of 

Assuming  no 
Hydration  of 
Solute      but 

Assuming  Hydration 

(8=51120 

/3=6H20 

Association  of 
Solvent 

Association  of 
Solvent 

Solvent 
not 
Associated 

Solvent 
Associated 

O.I 

2-59 

2.38 

2.38 

2.4I 

2.42 

2.42 

0.2 

5.06 

4.76 

4.76 

4-85 

4-90* 

4.90 

0-3 

7.6l 

7.14 

7-13 

7-33 

7-45 

7.40 

0.4 

10.14 

9-51 

949 

9.87 

10.07* 

9-94 

o-5 

12-75 

11.87 

11.84 

12.43 

12.78 

12.59 

0.6 

15-39 

14.24 

14.19 

15-05 

15-54* 

15.28 

0.7 

18.13 

16.59 

16-53 

17.71 

18.40 

17.97 

0.8 

20.91 

18.94 

18.85 

20.42 

21.32* 

20.76 

0.9 

2372 

21.29 

21.19 

23-15 

24-37 

23-55 

I.O 

26.64 

23.64 

23-50 

25.96 

27.50 

26.45 

Now  if  we  retain  the  idea  of  the  association  of  the  solvent, 
then  the  equation  becomes 


,        RT 

Po  =    TT 


n 


n 


Vm  N  - 
a 
*  Calculated  by  author  and  the  last  column  added. 


366  PHYSICAL   CHEMISTRY 

In  this  case  the  value  of  Vm,  the  molecular  volume,  would  be 

the  volume  (1000  —  18  0n)  grams  of  water  divided  by  — ^-@H 

a 

moles.  Upon  the  basis  of  these  two  formulae  and  on  the  as- 
sumption that  sugar  forms  a  pentahydrate,  values  for  the 
osmotic  pressure  have  been  calculated  from  Morse's  data 
and  are  incorporated  in  Table  LXII,  the  columns  being  fully 
explained  by  their  headings. 

In  the  last  column  there  are  added  the  calculated  values 
on  the  assumption  of  association  of  the  solvent,  that  the 
molecule  of  sugar  has  six  molecules  of  water  of  hydration, .and 
the  usual  value  (82.04)  of  R  is  employed.  With  these  as- 
sumptions the  calculated  values  approximate  very  closely 
to  the  observed  experimental  values  of  Morse. 

From  these  values  it  is  seen  that  by  introducing  into  the 
equation  for  ideal  solutions  factors  for  the  association  of  the 
solvent  and  the  hydration  of  the  sugar,  we  obtain  values  for 
the  osmotic  pressure  nearer  those  actually  obtained  experi- 
mentally than  the  values  given  in  the  third  column,  where 
these  assumptions  were  not  made.  Further,  the  hydration 
correction  is  much  more  pronounced  in  the  more  concen- 
trated solutions  than  the  association  factor  correction.  The 
same  is  noticed  if  the  data  of  Earl  of  Berkeley  and  Hartley 
are  employed  and  a  hexahydrate  of  sugar  be  assumed. 

Heat  of  Dilution.  —  More  than  ten  years  ago  Bancroft 
called  attention  to  the  relation  of  the  Heat  of  Dilution  and 
its  bearing  on  the  van't  Hoff-Raoult  Formula,  and  referred 
to  Ewan's  discussion  (1894)  of  this  problem  and  the  formula 
he  worked  out  showing  the  relation  of  the  heat  of  dilution  to 
the  osmotic  pressure,  which  had  been  practically  neglected. 
Bancroft  formulates  a  relation  and  proceeds  to  show  how  the 
osmotic  pressure  varies  with  the  heat  of  dilution,  that  the 
abnormal  molecular  weights  for  sodium  in  mercury,  sulphuric 
acid  in  water,  resorcinol  in  alcohol,  cupric  chloride  in  water, 
and  alcohol  in  benzene  are  due  wholly  or  in  part  to  the  heat 


CONCENTRATED   SOLUTIONS  367 

of  dilution,  but  the  abnormal  weights  for  sodium  chloride  in 
water  are  not  due  to  the  heat  of  dilution.  In  the  case  of 
sodium  in  mercury  the  apparent  molecular  weight  was  found 
to  be  16.5,  and,  correcting  for  the  heat  of  dilution,  22.7  was 
obtained.  The  apparent  molecular  weight  of  sulphuric  acid 
varies  from  57.7  in  a  5.6  per  cent  solution  to  11.7  in  a  68.5 
per  cent  solution,  and  when  the  correction  for  the  heat  of 
dilution  is  applied  we  get  molecular  weights  that  are  approxi- 
mately constant  but  somewhat  in  excess  (115)  of  the  true 
molecular  weight  (98),  and  increasing  at  first  and  then  re- 
maining practically  constant  with  the  increase  of  concen- 
tration. In  the  case  of  sodium  chloride  the  apparent  molec- 
ular weight  is  about  29,  or  one  half  of  the  formula  weight 
at  infinite  dilutions,  while  the  change  of  the  heat  of  dilution 
with  the  concentration  is  zero,  hence  these  abnormal  values 
for  sodium  chloride  are  real  and  are  not  to  be  explained  on  the 
basis  of  the  heat  of  dilution. 


CHAPTER  XXXI 
HYDRATION 

WE  have  seen  that  by  assuming  the  hydration  of  the  solute 
and  thus  removing  a  part  of  the  solvent  from  the  sphere  of 
action  as  solvent,  the  solution  becomes  more  concentrated, 
and  the  osmotic  pressure  calculated  on  this  basis  conforms 
more  nearly  to  the  values  determined  experimentally.  Jones 
and  his  students  ascribed  the  deviation  in  the  freezing  point 
determinations  to  the  formation  of  hydrates  and  assumed 
that  they  existed  only  in  concentrated  solutions.  In  the  case 
of  many  of  the  other  properties  of  solutions  which  are  colli- 
gative,  there  is  a  marked  difference  in  the  values  determined 
experimentally  and  calculated  upon  the  basis  of  the  Ar- 
rhenius  Electrolytic  Dissociation  Theory.  There  is  now  a 
tendency  to  explain  these  abnormal  results  upon  the  assump- 
tion of  the  union  of  the  solvent  and  the  solute,  i.e.  on  the 
assumption  of  the  existence  of  hydrates  in  solution.  This  is 
bringing  us  back  to  the  fundamental  conceptions  of  the  old 
Hydrate  Theory  of  Solutions  which  was  strongly  advocated 
by  Mendele"eff  (1886)  and  by  Pickering  (1890).  In  the 
foundation  of  the  old  Hydrate  Theory,  the  points  of  discon- 
tinuity in  the  plotted  observed  data  wherein  the  graphic 
method  was  employed  were  taken  as  evidence  of  the  existence 
of  hydrates.  Pickering  justified  this  method  and  fully  ap- 
preciated the  difficulties  in  its  application,  as  is  shown  from 
the  following  quotation : 

"  The  application  of  the  graphic  method  requires  a  great  amount  of 
care  and  a  close  attention  to  experimental  and  other  conditions,  and 
it  is  to  be  feared  that  hurried  use  of  it  by  those  who  have  not  taken  the 
trouble  to  master  the  necessary  details,  or  to  acquire  the  requisite 

368 


HYDRATION  369 

amount  of  skill,  may  bring  it  into  undeserved  disrepute.  From  the 
study  of  any  one,  or  any  few,  particular  breaks  I  concluded  nothing ; 
from  a  study  of  a  whole  series  of  density  results  I  only  concluded  that 
it  was  advisable  to  make  other  series  at  other  temperatures;  from  a 
study  of  the  series  at  four  different  temperatures  I  concluded  only  that 
I  had  '  strong  presumptive  evidence  '  of  the  existence  of  changes,  but 
that  confirmatory  evidence  from  the  study  of  independent  properties 
was  necessary  before  such  changes  could  be  regarded  as  established, 
and  it  was  only  after  obtaining  such  evidence  from  the  study  of  three 
or  four  properties  that  I  ventured  to  call  the  evidence  proof,  and  then 
only  with  oft-repeated  caution,  '  that  many  of  these  changes  were 
admittedly  of  a  very  doubtful  nature.'  " 

The  points  of  discontinuity  were  observed  in  the  case  of 
density  curves,  the  determination  of  capillarity,  viscosity, 
etc.  This  group  of  physical  properties  of  solutions  con- 
forms to  the  so-called  Law  of  Mixtures  and  is  additive  with 
respect  to  the  constituents.  Where  there  is  a  variation  from 
the  law  it  is  customary  to  assume  that  the  molecular  prop- 
erty of  the  solvent  remains  unchanged  and  to  ascribe  all 
deviations  to  changes  in  the  physical  property  of  the  solute, 
which  in  many  cases  has  led  to  absurd  conclusions.  To  get 
around  these,  complexes  between  the  solvent  and  solute 
have  been  assumed,  and  the  literature  contains  references 
to  a  large  number  of  such  cases  which  have  been  determined 
from  the  discontinuity  in  property-curves  of  the  following 
physical  properties  of  solutions :  heat  capacity,  density, 
viscosity,  refr activity,  conductivity,  compressibility,  surface 
tension,  coefficient  of  expansion,  and  heat  of  solution.  It 
would,  however,  lead  us  too  far  to  consider  in  detail  the  evi- 
dence presented  by  these  experimental  methods,  but  many 
experimenters  attribute  the  irregularities  in  the  property 
curves  to  the  presence  of  hydrates  and  use  these  properties 
for  proving  the  presence  of  hydrates  in  solution. 

In  Fig.  55  we  have  from  the  so-called  solubility  curve  for 
S03  in  H2O,  a  confirmation  of  the  "  breaks  "  of  Mendel£eff 
and  of  Pickering.  We  now  recognize  definite  hydrates  among 


370  PHYSICAL  CHEMISTRY 

which  it  is  possible  to  account  for  all  "  breaks  "  between 
10  and  go  per  cent  H2SO4  by  assuming  three  known  hydrates 
and  one  unknown  hydrate  instead  of  the  three  known  and 
six  unknown  hydrates  of  Pickering.  We  have  the  following 
well-defined  hydrates : 

1.  SO3  -1/2  H2O  is  very  stable  but  does  not  reveal  itself 
by  any  abrupt  change  in  the  density  curve,  but  the  capillar- 
ity and  the  viscosity  curves  both  reveal  it.     This  is  known  as 
pyro-sulphuric  acid  and  is  not  usually  considered  as  a  hydrate. 

2.  SOs  •  Ho>O,  a  monohydrate,  is  familiarly  known  as  sul- 
phuric acid  and  contains  100  per  cent  H2SO4. 

3.  H2SO4  •  H2O,  the  dihydrate  of  SO3,  is  scarcely  a  matter 
of  controversy. 

4.  H2SO4  •  2  H2O  has  been  obtained  in  the  crystalline  form. 

5.  H2SO4  •  4  H2O,  the  pentahydrate,  may  be  responsible 
for  breaks  at  59  per  cent. 

The  electrical  conductance  of  solutions  of  sulphuric  acid 
gives  a  curve  that  indicates  most  clearly  the  presence  of  three 
hydrates.  Water  and  the  trioxide  of  sulphur  are  both  ex- 
cellent insulators,  but  a  mixture  of  two  parts  of  SO3  to  four 
parts  of  H2O  is  one  of  the  best  conductors  known,  the  specific 
resistance  being  0.7388  ohm  at  18°  C.  The  curve  is  smoothly 
rounded,  and  according  to  Kohlrausch's  rule  that  mixtures 
give  higher  conductance  than  the  pure  substances,  there  is 
no  reason  for  attributing  this  maximum  to  the  formation  of 
hydrates  —  it  would  agree  fairly  well  with  the  formula 
SO3  •  1 8  H2O.  The  mixture,  on  changing  the  ratio,  decreases 
in  conductance  until  at  the  concentration  81.44  per  cent  SOs 
the  value  is  0.0080  ohm,  which  is  about  one  per  cent  of  the 
maximum  value.  This  minimum  is  very  clearly  defined,  as 
the  conductance  increases  100  per  cent  when  the  solution  is 
mixed  with  0.17  per  cent  of  H2O  or  with  0.23  per  cent  of  H2O. 
Kohlrausch  has  shown  that  this  minimum  is  reached  when 
the  SO3  and  H2O  are  in  the  ratio  of  0.9975  :  i,  which  is  virtu- 
ally i :  i,  and  therefore  this  minimum  can  be  attributed  to 


HYDRATION  371 

the  hydrate  SO8  •  H2O,  which  is  a  chemical  compound  and  is 
an  insulator.  The  hemi-hydrate  2  SO3  •  H2O  has  even  a 
lower  conductance  (0.0008)  than  the  monohydrate,  and  solu- 
tions of  SO3  in  this  give  zero  conductance.  The  minimum 
value  at  69  per  cent  SOs  corresponds  to  the  dihydrate 
SO3  •  2  H2O,  the  conductance  at  18°  being  0.098  ohm,  and 
this  minimum  is  300  times  less  sensitive  than  in  the  case 
of  the  monohydrate. 

It  will  be  recalled  that  the  Arrhenius  Theory  of  Electro- 
lytic Dissociation  was  advanced  to  account  for  the  abnormal 
values  that  are  obtained  by  the  lowering  of  the  freezing  point, 
the  elevation  of  the  boiling  point,  the  osmotic  pressure,  and 
the  lowering  of  the  vapor  pressure.  The  degree  of  electro- 
lytic dissociation  could  be  determined  with  equal  accuracy 
by  these  various  methods  and  also  by  the  electrical  conduc- 
tivity. These  properties  of  solutions  are  Colligative,  that  is, 
they  depend  upon  the  number  of  parts  in  the  solution,  and, 
the  solutes  are  said  to  be  ionized  in  order  to  account  for  these 
additional  parts  in  solution. 

What  is  the  cause  of  this  ionization  ?  One  of  the  questions 
that  has  been  asked  frequently  is,  Why  is  it  that  these  sub- 
stances which  liberate  so  much  heat  when  they  are  formed 
become  dissociated  so  easily  when  they  are  dissolved?  In 
other  words,  what  is  the  motive  of  the  electrolytic  dissocia- 
tion? In  the  formation  of  KC1  from  its  elements  there  is 
a  liberation  of  105,600  calories,  which  means  an  absorption 
of  this  same  amount  of  heat  when  the  compound  is  again 
decomposed,  but  the  heat  of  electrolytic  dissociation  is  given 
as  250  calories.  Bonsfield  says  : 

"  This  extraordinary  discrepancy  between  the  two  values  appears 
to  indicate  that  the  process  of  ionization  cannot  consist  merely  of  the 
separation  of  the  molecule  into  its  constituent  atoms  even  though 
they  may  be  endowed  with  electrical  charges,  and  we  are  driven  to 
assume  that  the  essentially  endothermic  process  of  dissociation  must 
be  balanced  by  some  powerful  exothermic  action,  associative  rather 
than  dissociative." 


372  PHYSICAL  CHEMISTRY 

Fitzgerald  in  his  classic  Helmholtz  Memorial  Lecture  de- 
livered in  1892  says : 

"  Why  is  there  then  so  little  heat  absorbed  when  ions  are  dissociated 
by  going  into  solution  ?  It  has  been  proposed  to  explain  this  by  various 
suggestions  which  do  little  more  than  re-state  the  facts  in  some  other 
form  and  call  for  new  properties  of  ions  especially  invented  to  suit  the 
circumstances.  The  suggestion  mentioned  is  that  the  presence  of  a 
body  of  high  specific  inductive  capacity,  like  water,  very  much  di- 
minishes the  force  of  the  attraction  between  the  electrons  by  providing, 
what  comes  to  the  same  thing,  induced  electrons  in  the  water  mole- 
cules to  help  in  drawing  those  in  the  salt  apart.  This  is  an  excellent 
suggestion ;  but  is  it  not  really  the  same  thing,  under  another  guise, 
as  stating  that  it  is  by  chemical  combination  with  water  that  the  salt 
has  conferred  upon  it  the  property  of  exchanging  partners  ?  What  are 
these  electric  charges  supposed  to  be  induced  on  water  but  electrons 
thereon  ?  and  what  is  the  attraction  of  the  electrons  among  the  mole- 
cules but  another  name  for  chemical  combination  ?  All  of  this  hangs 
together,  but  it  lends  no  support  at  all  to  the  dynamically  impossible 
theory  that  the  ions  are  free.  What  it  suggests  is  that  this  so-called 
freedom  is  due  to  there  being  complete  bondage  with  the  solvent." 

At  the  time  Arrhenius  published  the  relative  values  of  i 
and  a  calculated  from  the  electrical  conductance,  the  freezing 
point,  and  the  boiling  point  determinations,  he  recognized 
great  discrepancies  in  the  cases  of  the  sulphates  in  general, 
which  he  sought  to  explain  by  assuming  polymerization  of 
the  undissociated  molecules.  Since  the  data  employed  by 
Arrhenius  were  obtained,  more  accurate  data  have  been  col- 
lected, showing  that  these  abnormal  values  are  real.  The 
freezing  point  determinations  by  Loomis,  Abegg,  Jones,  Roth, 
Raoult,  Ewan,  Kahlenberg,  Biltz,  as  well  as  boiling  point 
determinations  by  the  same  experimenters,  and  particularly 
the  data  by  Smits,  show  that  these  methods  give  values  for 
the  degree  of  electrolytic  dissociation  which  are  in  many  cases 
entirely  different  from  the  values  obtained  by  the  conductiv- 
ity method.  A  few  specific  cases  will  suffice  to  illustrate  the 
general  trend  of  these  irregularities.  The  data  given  in  Table 
LXIII  are  taken  from  that  compiled  in  Landolt  and  Born- 


HYDRATION 


373 


stein's  Tabellen  with  the  exception  of  that  for  KBr  and  some 
of  the  data  for  NaCl  by  the  boiling  point  method,  which  were 
obtained  from-  the  original  source.  The  degree  of  dissociation 
from  the  electrical  conductance  method  are  taken  partially 
from  Jones'  work,  and  the  other  values  were  calculated  from 
data  given  in  Landolt  and 


TABLE  LXIII 
FREEZING  POINT  OF  SOLUTIONS 


GRAM  ANHYDROUS 
SALT  IN  100  GR.  H-iO 

FREEZING 
POINT 
LOWERING 

MOLECULAR 
WEIGHT 

DEGREE  OF  DISSOCIATION 

From  Freezing 
Point 

From  Electrical 
Conductance 

NaCl,  Molecular  Weight  58.5 


0.01047 

0.006403° 

30.4 

92.4 

94 

0.03738 

0.02339 

29.0 

101.7 

9i 

0.1250 

0.07584 

30.6 

91.2 

85 

0.4887 

0.2897 

31.4 

86.3 

79 

1.479 

0.8615 

31-9 

83.3 

68 

5.770 

3-293 

32.6 

79.6 

MgSO4,  Molecular  Weight  120.4 


0.00141 

0.000433 

60.6 

98.7 

0.00813 

O.OO222I 

68.1 

76.8 

0.1520 

0.03430 

82.4 

46.1 

2.534 

0.469 

100.5 

19.8 

75 

5-994 
9.768 

I.OO6 
1.629 

110.8 
111.5 

8.7 
8 

55 
44 

Jones 

18.343 

3-471 

98.3 

22.5 

32 

ZnSO4,  Molecular  Weight  161.5 


0.00644 

0.001387 

109 

48.2 

0.08333 

0.01499 

103.4 

56.2 

0.2246 

0.03701 

113 

42.9 

2.063 

0.285 

134 

20.5 

44] 

5.026 

0.625 

149-5 

8.0 

33      Jones 

16.169 

1.87 

1  66 

26] 

* 


374 


PHYSICAL   CHEMISTRY 


From  the  data  obtained  by  the  freezing  point  method  the 
molecular  weight  of  NaCl  is  practically  constant  for  all  con- 
centrations, showing,  however,  a  slight  decrease  in  the  degree 
of  dissociation  with  the  increased  concentration  up  to  about 
molar  concentrations.  At  the  lower  dilutions  the  degree 
of  dissociation  as  calculated  from  the  conductance  agrees 
very  well  with  that  obtained  from  the  freezing  point  data, 
but  at  the  higher  concentrations  there  begins  to  appear  a 
marked  divergence.  For  MgSO4  the  degree  of  dissociation 
decreases  very  rapidly  with  the  concentration  and  becomes 
only  a  few  per  cent  at  approximately  normal  concentration. 
The  conductance  gives  at  these  higher  concentrations  a  degree 
of  dissociation  of  about  40  per  cent.  Practically  the  same 
holds  for  ZnSO4,  at  molar  concentration  the  degree  of  dissocia- 
tion is  practically  zero  according  to  the  freezing  point  determi- 
nations and  26  per  cent  by  the  electrical  conductivity  method. 

TABLE   LXIV 
BOILING  POINT  DETERMINATIONS 


GRAM  ANHYDROUS 
SALT  IN 

100  GR.    HzO 

RISE  OF 
BOILING  POINT 

MOLECULAR 
WEIGHT 

DEGREE  OF  DISSOCIATION 

From  Boiling 
Point 

From  Electrical 
Conductance 

NaCl,  Molecular  Weight  58.5 


0.4388 

0.074° 

30.91 

89-3 

86 

0.747 

0.119 

32.7 

78.9 

84 

2.158 

0.351 

32.0 

82.8 

77 

4.386 

0.717 

31.8 

84 

7i 

7.27 

1-235 

29.9 

95-7 

66 

12.17 

2.182 

29.0 

101.7 

59 

18.53 

4.032 

26.7 

119 

48.5 

31.242 

6.82 

24.1 

142.7 

38 

KBr,  Molecular  Weight  119.1 


2.614 

0.206 

66.0 

80.5 

82.2 

5.504 

0-433 

66.1 

80.2 

79-5 

9-593 

0.763 

65-4 

82.1 

77 

23-393 

1.968 

61.8 

92.7 

72.4 

33.278 

2.899 

SQ-7 

99-5 

60.0 

43.418 

3-932 

57-4 

107-5 

65.8 

51-204 

4-778 

55-7 

"3-7 

63.2 

HYD  RATION 

TABLE  LXIV  —  Cont. 

MgCb,  Molecular  Weight  95.3 


375 


3-371 

0.416° 

42.1 

61.1 

60 

6.199 
13-87 

0.850 
2.380 

37-9 
30-3 

75-7 
107.2 

43  1  Jones 

22.06 

4.720 

24-3 

146.1 

3iJ 

BaClz,  Molecular  Weight  208.3 


3-397 

0.208 

84.9 

72.8 

72 

8.777 

0-525 

86.6 

70.2 

64.8 

18.619 

1.174 

82.5 

76.2 

58.5 

35-036 

2.517 

72.4 

••      86.9 

52 

S4-.SI9 

4-157 

68.2 

102.9 

45 

CuSO4,  Molecular  Weight  159.7 


3.356 

0.091 

191.8 

7.811 

0.189 

214.9 

15.952 

0.374 

22J.8 

32.36 

0.874 

192.5 

39.57 

1.192 

172.6 

56.95 

2.283 

129.7 

73.77 

3.768 

101.8 

Cane  Sugar,  Molecular  Weight  342 


2.447 

0.035 

363-5 

4.316 

0.064 

350.7 

7.25 

0.103 

366 

1  1.  02 

0.164 

349-4 

14.82 

0.240 

321 

21.66 

0.363 

310.0 

36.15 

0-55 

342 

65.97 

1.13 

304 

100.95 

1.853 

283 

I75-I 
276.2 

3.84 
6.71 

237 
214 

Boiling  point  data  are  given  in  Table  LXIV  for  NaCl,  KBr, 
MgCl2,  BaCl2,  CuSO4,  and  sugar.  The  molecular  weight  for 
NaCl  decreases  with  the  increased  concentration,  giving  a 
dissociation  increasing  with  the  increased  concentration. 
For  concentrations  of  about  three  to  five  molar,  the  degree  of 
dissociation  calculated  from  the  boiling  point  data  gives  over 
140  per  cent,  while  according  to  the  conductivity  method  the 
dissociation  is  from  48  to  38  per  cent  respectively.  For 


376  PHYSICAL   CHEMISTRY 

KBr  the  same  is  true,  for  concentrations  2.8  to  4.3  molar  the 
degree  of  dissociation  ranges  from  99.5  per  cent  to  114.9, 
while  according  to  the  conductivity  method  the  values  for 
the  same  concentrations  are  69  and  63.2  per  cent  respectively. 
For  MgCl2  the  molecular  weight  decreases  with  increased 
concentration,  giving  a  dissociation  increasing  with  con- 
centration, being  at  approximately  2  molar  concentration 
146  per  cent  as  against  about  31  per  cent  as  determined  by 
Jones.  For  BaCl2  the  molecular  weight  decreases  as  the  con- 
centration is  increased,  showing  a  dissociation  ranging  from 
53  per  cent  for  approximately  0.15  molar  solution  to  103  per 
cent,  while  for  the  same  concentrations  the  degree  of  dissocia- 
tion by  the  electrical  conductivity  method  is  7  2  per  cent  and 
45  per  cent  respectively.  For  CuSO4  the  molecular  weights 
are  all  above  that  represented  by  the  formula  weight  except 
at  the  very  highest  concentration  which  is  nearly  5  molar. 
There  would  be  no  dissociation  at  the  lower  concentration, 
but  at  the  higher  concentrations  the  molecular  weight  found 
is  lower  than  the  theoretical  value.  The  same  is  also 
found  for  the  non-electrolyte  sugar,  the  molecular  weight 
decreases  with  increased  concentration.  In  the  dilute  solu- 
tions the  molecular  weight  is  about  normal,  while  at  about  8 
molar  concentration  the  value  is  214. 

By  the  vapor  pressure  measurements  at  o°  Dieterici  found 
that  the  molecular  lowering  for  CaCl2  diminished  rapidly  with 
the  increase  of  dilution,  and  at  about  o.i  N  concentration 
increased  with  the  dilution.  The  freezing  point  determina- 
tions of  Loomis  and  of  Ponsot  show  a  minimum  for  the  mo- 
lecular lowering  of  the  freezing  point  at  nearly  the  same 
concentration.  Jones  and  Chambers'  results  confirm  this. 
For  H3PO4,  H2SO4,  NaCl,  CaCl2,  cane  sugar,  dextrose,  and 
urea  in  concentrations  o.i  to  i.o  N,  Dieterici  found  that  the 
molecular  lowering  of  the  vapor  pressure  diminishes  as  the 
dilution  increases,  which  is  opposite  to  that  required  by  the 
electrolytic  dissociation  theory  as  stated.  Dieterici  therefore 


HYDRATION  377 

refrains  from  even  attempting  to  make  any  further  compari- 
son between  the  degree  of  dissociation  as  calculated  from  the 
vapor  pressure  measurements  on  the  one  hand  and  the  con- 
ductivity on  the  other.  From  vapor  pressure  determinations 
Lincoln  and  Klein  found  practically  the  same  values  for  the 
molecular  weight  of  KNO3  as  that  found  by  other  workers 
by  the  freezing  point  and  boiling  point  methods.  For  NaNO3, 
however,  the  value  for  the  molecular  weight  was  practically 
the  same,  48.13-48.91,  over  the  whole  range  of  concentra- 
tion. This  is  approximately  one  half  the  theoretical  value, 
85.1,  and  the  degree  of  dissociation  would  be  the  same  for  the 
whole  range  of  concentration.  For  the  most  concentrated 
solutions  of  LiNOs  the  molecular  weight  was  found  to  be 
17.58,  and  for  the  most  dilute,  36.09,  as  compared  to  the 
formula  weight,  69.07.  In  the  most  dilute  solutions  the 
molecular  weight,  34.5,  is  practically  one  half  the  theoretical 
value,  giving  a  degree  of  dissociation  virtually  of  100  per  cent, 
while  for  the  most  concentrated  solutions  employed  the 
value  17.35  found  is  about  one  fourth  the  molecular  weight 
and  would  correspond  to  a  dissociation  of  about  200  per  cent. 
By  the  freezing  point  method  Biltz  found  the  same  general 
results,  i.e.,  in  the  more  highly  concentrated  solutions  the 
LiNO3  is  the  more  highly  dissociated. 

Various  explanations  have  been  put  forth  to  account  for 
these  numerous  irregularities  such  as  illustrated  above,  and 
there  is  one  marked  similarity  in  them.  They  all  aim  to 
explain  these  anomalous  results  upon  the  assumption  of  some 
combination  between  the  solvent  and  the  dissolved  substance. 

Arrhenius  was  among  the  first  to  suggest  that  ionization 
depends  not  on  the  physical  properties  of  the  solvent  but 
upon  the  chemical  equilibrium  between'  the  solute  and  the 
solvent.  As  early  as  1872  Coppet,  from  his  freezing  point 
measurements,  ascribed  his  results  to  the  formation  of 
hydrates,  and  calculated  the  composition  of  many  of  them. 
Jones  ascribes  the  deviation  in  the  freezing  point  determina- 


378  PHYSICAL  CHEMISTRY 

tions  to  the  formation  of  hydrates,  but  assumes  that  they 
exist  only  in  concentrated  solutions.  He  assumes  that  the 
degree  of  hydration  can  be  calculated  upon  the  normal 
volume  plan,  notwithstanding  that  this  method  involves 
the  acceptance  of  the  Ionic  Hypothesis  and  the  application 
throughout  of  the  factor  18.6  in  calculating  the  lowering 
of  the  freezing  point.  Jones  also  leaves  out  of  account  the 
effect  of  hydration  on  the  ionic  mobility,  the  polymerization 
effects,  and  practically  all  others,  and  concentrates  the  whole 
variation  to  the  formation  of  hydrates  resulting  in  the  re- 
moval of  part  of  the  water  from  its  function  as  a  solvent. 
"  The  fact  that  a  part  of  the  water  is  combined  with  the  dis- 
solved substance  and  is  not  acting  as  solvent,  must  be  taken 
into  account  in  dealing  with  all  solutions  and  especially  con- 
centrated ones.  This  accounts  in  large  part  for  the  abnormal 
behavior  of  concentrated  solu tions. "  "  We  conclude  that 
both  molecules  and  ions  have  the  power  to  combine  with 
water  in  aqueous  solutions  and  form  hydrates."  In  many 
cases  the  solvent  "  combined  "  amounts  to  a  large  percentage 
of  the  water  present  and  in  a  few  cases  to  between  100  per 
cent  and  114  per  cent. 

Biltz,  although  he  pointed  out  that  Nernst  had  shown  that 
the  formation  of  hydrates  is  directly  contrary  to  the  Law 
of  Mass  Action,  and  consequently  untenable,  recognizes  that 
their  formation  may  be  the  cause  of  the  abnormal  properties 
of  strong  electrolytes.  He  argued  that  CsN03  to  be  slightly 
hydrated,  if  at  all,  lowers  the  freezing  point  in  accordance 
with  the  Ostwald  Dilution  Law  and  is  to  be  regarded  as  be- 
having normally.  The  electrical  conductance  of  such  solu- 
tions is  not  that  to  be  expected  from  the  freezing  point  deter- 
minations, and  it  therefore  follows  that  conductivity  cannot 
be  taken  as  a  true  measure  of  the  state  of  dissociation  even 
in  the  case  of  salts  that  are  not  hydrated.  Taking  the  cases 
of  NaCl  and  KC1,  which  do  not  conform  to  the  dilution  law 
as  regards  freezing  point,  and  assuming  that  they  are  dis- 


HYDRATION  379 

sociated  to  about  the  same  extent  as  CsN03,  Biltz  calculated 
that  NaCl  can  be  associated  with  19  to  20  molecules  of  water 
and  KC1  with  15  to  24  molecules,  according  to  the  concentra- 
tion. Biltz,  as  well  as  Jones,  finds  indications  that  the  com- 
plexity of  the  hydrates  decreases  with  rise  of  temperature. 
The  abnormal  boiling  point  values  are  explained  upon  the 
basis  of  the  formation  of  hydrates. 

Smits  determined  the  vapor  pressure  at  o°  of  NaCl,  H2SO4, 
KNO3,  and  sugar.  For  sugar  he  finds  an  average  molecular 
hydration  of  5.7  as  compared  to  6.0  obtained  by  the  freezing 
point  method,  hence  we  would  conclude  that  sugar  exists  in 
solution  as  a  hexahydrate.  Compare  this  with  the  assumed 
hydration,  page  365. 

Abegg  has  stated  very  clearly  the  application  of  the  hydrate 
theory  to  the  equilibrium  between  the  solvent  and  solute, 
and  his  researches  show  that  what  is  ordinarily  termed  normal 
or  simple  ionization  may  be  to  a  very  large  extent  a  complex 
ionization  in  which  the  solvent  molecules  play  an  essential 
part.  He  assumes  that  the  molecules  possess  a  power  of 
spontaneous  ionization  which  is  independent  of  the  associa- 
tion of  the  ions  with  the  solvent. 

Armstrong  says  that  apart  from  the  fact  that  the  Elec- 
trolytic Dissociation  Theory  is  irrational  and  inapplicable 
to  compounds  in  general,  there  are  experimental  facts  ob- 
tained by  several  different  lines  that  militate  against  it. 
Sucrose  and  esters  are  hydrolyzed  in  the  presence  of  acids 
and  also  of  enzymes,  and  in  both  cases  the  degree  of  acidity 
varies  with  the  acid  or  with  the  enzyme.  Since  the  selective 
action  of  the  enzymes  can  be  explained  on  the  basis  of  com- 
bination with  the  hydrolyte,  there  is  no  reason  why  this  ex- 
planation should  not  be  extended  to  the  acids.  Further,  it  is 
found  that  the  acidity  of  an  acid  as  a  hydrolyzing  agent  is 
frequently  increased  by  the  addition  of  its  neutral  salts,  and 
as  non-electrolytes  also  sometimes  act  in  the  same  way  there 
is  no  reason  to  account  for  the  activity  of  the  electrolytes  by 


380  PHYSICAL   CHEMISTRY 

an  explanation  which  is  inapplicable  to  non-electrolytes. 
Since  alcohol,  equally  with  hydrochloric  acid,  causes  the  pre- 
cipitation of  chlorides  from  solution,  the  explanation  which 
can  be  applied  to  alcohol,  —  namely,  hydration  formation,  — 
should  also  be  applicable  to  hydrochloric  acid. 

In  1886  Armstrong  attributed  the  increased  molecular 
conductivity  of  dilute  solutions  to  the  gradual  resolution  of 
the  more  or  less  polymerized  molecules  of  the  salt  into  simpler 
molecules  or  monads  which,  when  combined  with  the  solvent, 
constituted  a  "  composite  electrolyte."  Recently  he  adds 
that  "  the  electrolytically  effective  monads  must  be  thought 
of  as  hydrated  in  some  particular  manner,  perhaps  as  hydrox- 
ylated  and  that  the  association  of  the  solvent  with  the  nega- 
tive radical  of  the  solute  was  the  determining  factor  in  elec- 
trolysis." He  considers  that  the  positive  radical  of  the 
solute  has  no  tendency  to  associate  with  the  solvent  and  that 
the  power  of  ionization  does  not  involve  the  resolution  of  the 
molecules  into  separate  ions. 

Werner  in  his  New  Ideas  on  Inorganic  Chemistry  presents  a 
re'sume'  of  his  work  on  the  ammonia  substitution  products  and 
the  reactions  in  the  formation  of  analogous  compounds,  which 
he  develops  into  his  theory  of  Bases  and  Acids  and  the  Theory 
of  Hydrolysis,  etc.  In  this  he  presents,  in  opposition  to  the 
above  idea,  the  suggestion  that  the  ionization  is  due  to  the 
association  of  molecules  of  water  or  ammonia  with  the  metal, 
the  negative  radicals  being  regarded  as  inert.  Many  metallic 
salts  form  hydrates  with  six  molecules  of  water  such  as  the 
following:  [Ni(OH2)6]Cl2,  [Co(OH2)6]Cl2,  [Zn(OH2)6](NO3)2, 
[Mg(OH2)6]Br2,  [Ca(OH2)6]Cl2,  [Sr(OH2)6]Br2,  [Fe(OH2)6]Cl3. 
Many  of  these  hydrates  contain  the  maximum  number 
of  water  molecules  known  to  the  salt,  and  their  con- 
stitution is  analogous  to  the  hexamine  metallic  salts  which 
have  been  extensively  studied.  Werner  assumes,  there- 
fore, that  the  hexahydrates  are  salt-like  compounds  in 
which  the  positive  radical  consists  of  complexes  containing 


HYDRATION  381 

the  metal  and  six  molecules  of  water,  which  are  linked 
directly  to  the  metallic  atom  and  in  a  separate  sphere  from  the 
acid  residues.  The  greenish  blue  hexahydrate  CrCl3  •  6  H2O 
dissolves,  giving  a  blue-violet  solution,  and  all  three  of  the 
chlorine  atoms  are  present  as  ions,  as  is  shown  by  the  elec- 
trical conductivity  and  freezing  point  determinations  and  by 
treatment  with  silver  nitrate.  It  is  therefore  represented 
by  the  formula  [Cr(OH2)6]Cl3.  On  losing  two  molecules  of 
water  this  is  transformed  into  a  green  hydrate,  CrCl3  •  4  H2O. 
This  hydrate  in  solution  shows  that  only  part  of  its  chlorine 
is  in  the  ionogen  condition  as  only  two  thirds  of  the  chlorine 
can  be  precipitated  by  AgNO3.  The  formula  would  then  be 

l2-H2O.     There   is   still  another  hexahydrate 


which  contains  only  one  chlorine  with  ionogen  properties, 
and  the  formula  assigned  to  it  is  Cr/QH\  Cl  2  H2O. 

These  extra  molecules  of  water  are  not  linked  to  the  disso- 
ciated chlorine  ions,  and  from  evidence  presented  he  concludes 
that  they  belong  in  some  way  to  the  chromium  complex,  and 
the  following  expression  illustrates  the  relations  between  these 
three  isomeric  hexahydrates  : 


[< 


1  •  H20~| 

[Cr  (OH2)6]C13   |  Cr  ^wT  I C12   |  Cr  Cl  •  H2O  Cl 

(OH2)4  J 

Blue  hydrate  of  Bierrum's  chloride  Green  hydrate  of 

chromium  chloride  chromium  chloride 

Werner  further  shows  that  acids  as  well  as  bases  are  formed 
through  the  combination  of  the  solvent  and  solute,  so  in  gen- 
eral he  expresses  the  view  that  the  ionization  is  preceded  by 
a  combination  with  the  solvent.  t  It  is  primarily  the  metallic 
or  positive  part  of  the  solute  that  is  hydrated. 

It  would  lead  us  too  far  to  consider  the  experimental  data 
that  led  Tammann  to  consider  that  salt  solutions  resemble 
the  pure  solvent  under  increased  external  pressure ;  Traube 


382  PHYSICAL   CHEMISTRY 

to  state  that  each  ion  is  in  combination  with  a  single  molecule 
of  water ;  Vaillant  from  density  determinations  to  conclude 
most  ions  to  be  anhydrous,  but  OH",  F~,  S~~,  and  CO3~  to 
be  monohydrated ;  Philip  to  deduce  from  solubility  of  hy- 
drogen and  oxygen  in  salt  solutions  the  agreement  of  the 
degree  of  hydration  with  the  values  obtained  by  the  acceler- 
ation of  the  inversion  of  cane  sugar  by  acids  as  influenced 
by  salts  as  measured  by  Caldwell  and  from  the  freezing 
point  determinations  by  Bonsfield  and  Lowry ;  and  to  show 
how  the  Phase  Rule  could  be  applied  to  the  determination 
of  hydrates  in  solution. 

Kohlrausch's  observation  led  him  to  consider  the  ions 
water  coated  and  that  the  combined  water  altered  the  size 
of  the  ions,  and  he  concluded  that  the  effect  of  the  change 
of  velocity  and  of  size  of  the  ions  might  adequately  account 
for  the  change  in  the  migration  velocity  observed  with  the 
change  in  the  dilution,  i.e.  that  there  is  a  change  in  the  degree 
of  hydration  of  the  ion  with  the  change  in  the  concentration 
of  the  solution.  From  Table  XLIX  of  Transference  numbers 
it  appears  that  the  heavier  atoms  yield  the  more  mobile  ions, 
and  for  this  reason  it  is  concluded  that  the  ions  are  hydrated. 
Lithium  ion  is  the  most  highly  hydrated  and  the  caesium  ion 
the  least  hydrated  of  the  metals  of  the  alkalies. 

When  a  current  is  passed  through  the  solution  of  an  elec- 
trolyte the  transfer  of  the  current  should  be  accompanied  by 
the  transfer  of  water  if  the  ions  are  hydrated,  and  it  should  be 
an  easy  matter  to  detect  this.  Various  attempts  have  been 
made  to  determine  this  transfer  of  water  by  electrolyzing  a 
solution  containing  a  small  quantity  of  a  non-electrolyte  that 
could  be  used  as  a  reference  substance.  This  reference 
substance  not  being  affected  by  the  current  will  remain 
distributed,  after  the  electrolysis,  just  as  before,  and  any 
change  resulting  from  the  transference  of  the  water  from 
the  anode  chamber  will  be  recognized  by  an  increase  in  the 
concentration  of  the  non-electrolyte  at  the  anode  and  a  cor- 


HYDRATION  383 

responding  decrease  at  the  cathode.  As  no  change  takes 
place  when  the  electrolyte  is  absent,  it  is  assumed  that  the 
water  is  transported  by  the  migrating  ions  and  that  this  is 
the  amount  of  water  that  is  in  combination  with  the  respec- 
tive ions.  Nernst  and  his  pupils  have  tried  this  method  with 
indifferent  success.  Washburn  found  that  the  cations  are 
hydrated  as  follows:  H(H2O)0.3,  K(H2O)i.8,  Na(H2O)2.o, 
Li(H2O)4.7.  Ganard  and  Oppermann  have  found  by  as- 
suming the  hydrogen  ion  to  be  anhydrous  the  following  values 
of  hydration  for  some  of  the  anions :  SO4(H20)9,  C1(H2O)B, 
Br(H2O)4,  NO3(H2O)2.5.  Newberry1  states:  "  Previous  de- 
terminations of  the  hydration  of  ions  by  observations  of  the 
change  of  concentration  of  the  non-electrolyte  present  have 
given  incorrect  values  due  the  transport  of  the  non-electro- 
lyte by  the  ion  present  and  also  by  the  action  of  electric  en- 
dosmosis."  He  concludes  from  a  study  of  metal  over  volt- 
age that  H,  OH,  Fe,  Ni,  and  Co  ions  are  hydrated  in 
aqueous  solution  while  Cu,  Ag,  Zn,  Cd,  Hg+,  Tl,  Pb,  Sn,  NH4, 
Na,  K,  Cl,  NO3,  SO4  ions  are  not  hydrated. 

Constitution  of  Water.  —  We  have  seen  on  several  occa- 
sions that  water  was  considered  a  highly  associated  liquid, 
and  the  exact  composition  of  the  associated  molecules  has 
been  the  subject  of  extensive  research.  As  early  as  1891, 
Rontgen  put  forth  the  idea  that  water  is  a  binary  mixture  of 
"  water  molecules  "  and  of  "  ice  molecules  "  of  greater  com- 
plexity but  smaller  density,  so  that  when  the  liquid  is  heated 
these  complexes  are  decomposed,  and  a  contraction  is  pro- 
duced which  is  sufficient  between  o°  and  4°  to  counteract  the 
ordinary  thermal  expansion  of  the  liquid.  Tammann  made 
use  of  the  composite  character  of  liquid  water  to  account  for 
the  abnormal  character  of  his  data  obtained  on  the  com- 
pressibility of  the  liquid,  and  also  regarded  water  as  a  binary 
mixture.  Sutherland,  within  the  last  few  years,  from  his  ex- 
tensive researches,  concludes  that  water  vapor  in  the  condi- 

1  Jour.  Chem.  Soc.  in,  470  (1917). 


384  PHYSICAL  CHEMISTRY 

tion  of  a  nearly  perfect  gas  is  hydrol  (H2O),  ice  is  trihydrol 
(H2O)a,  and  liquid  water  is  a  mixture  of  the  trihydrol  and 
dihydrol  (H2O)2  in  proportions  which  vary  with  the  tempera- 
ture, pressure,  and  the  presence  of  solutes.  It  is  to  this  com- 
plex character  of  water  that  many  of  the  exceptional  proper- 
ties of  water  and  of  aqueous  solutions  are  attributed. 

Bonsfield  and  Lowry,  from  a  study  of  the  density  of  aqueous 
solutions  of  caustic  soda,  sugar,  chloral,  acetic  acid,  silver 
nitrate,  sodium  chloride,  potassium  chloride,  lithium  chloride, 
and  calcium  chloride,  conclude  that  water  is  really  a  ternary 
mixture  consisting  of  the  trihydrol,  dihydrol,  and  monohy- 
drol.  On  cooling  liquid  water  there  is  a  formation  of  the 
more  polymerized  ice  molecules,  and  heating  causes  their 
dissociation,  yielding  the  monohydrol  or  steam  molecules. 
Each  of  these  changes  is  accompanied  by  an  increase  of 
volume  superimposed  upon  the  expansion  or  contraction  re- 
sulting from  the  mere  temperature  change.  Hence  the 
density  of  solutions  is  presented  as  evidence  of  the  formation 
of  hydrates.  It  is  argued  that  the  influence  of  the  solute 
cannot  be  accounted  for  unless  some  abnormal  value  is  as- 
signed to  the  density  of  water  in  combination  with  the  solute. 
Hydrate  formation  is  stated  to  be  always  accompanied  by 
a  contraction  of  volume,  hence,  the  density  of  this  water  must 
be  greater  than  that  of  the  water  in  the  ordinary  state.  In 
1875  F.  W.  Clark  attributed  to  water  of  crystallization  a 
molecular  volume  of  14  cc.,  and  this  is  practically  the  same 
as  that  deduced  by  Thorp  and  Watts  from  the  metallic  sul- 
phates, which  was  14.5  cc.  These  values  give  a  density  of 
approximately  1.24  for  the  water  of  crystallization.  Suther- 
land gives  1.089  as  the  density  of  dihydrol,  and  Bonsfield  cal- 
culates the  density  of  water  of  hydration  of  KC1  as  i .  i ,  which 
value  gives  a  degree  of  hydration  of  this  salt  practically  the 
same  as  the  value  found  by  Philip  from  the  solubility  of  hy- 
drogen gas  in  KC1  solutions  and  that  of  Caldwell  from  the 
influence  of  KC1  in  accelerating  the  inversion  of  cane  sugar 


HYDRATION  385 

by  acids.  Hence  they  conclude  that  the  density  of  combined 
water  approximates  that  of  the  denser  constituent  of  liquid 
water. 

Guye,  from  his  extensive  experimentation  on  vapor  pres- 
sure, surface  tension,  molecular  weight  determinations,  and 
association  coefficients,  concludes  that  the  data  obtained 
appear  to  form  new  evidence  in  favor  of  the  chemical  concep- 
tion of  the  phenomenon  of  association  or  polymerization  in 
the  liquid  phase  of  water  or  other  associated  liquids.  And 
further,  the  coefficient  of  association  of  Dutoit  and  Majoin 
is  in  agreement  with  the  results  according  to  which  liquid 
water  at  o°  is  mostly  t'rihydrol,  (H2O)3,  and  at  the  boiling 
point  dihydrol,  (H2O)2. 

Walden  from  his  researches  on  the  anomalous  behavior  of 
water  when  dissolved  in  solvents  of  high  dielectric  constants 
concludes  that  a  chemical  interpretation  of  these  results  must 
be  attempted  and  that  there  is  formed,  owing  to  the  chemical 
nature  of  the  solvent  and  solute,  a  molecular  combination  of 
a  salt  character  which  is  then  the  conductor  of  the  electric 
current  and  an  electrolyte. 

From  the  foregoing  we  see  that  there  is  a  tendency  for  the 
modern  workers  to  get  back  to  the  earlier  conception  of  a  re- 
action between  the  solvent  and  the  solute,  and  that  the  formu- 
lation of  any  theory  of  solutions  should  take  this  into  con- 
sideration. 


CHAPTER  XXXII 
HYDROLYSIS 

WE  are  familiar  with  the  fact  that  a  solution  of  Na2C03 
is  alkaline  in  reaction ;  but  Na2CO3  is  denned  as  a  normal 
salt,  i.e.  one  in  which  all  of  the  hydrogen  of  the  acid  had  been 
replaced  by  sodium.  We  further  define  a  substance  which 
in  aqueous  solutions  yields  hydroxyl  ions  a  base,  and  con- 
versely, since  there  are  hydroxyl  ions  in  a  solution  of  Na2CO3, 
it  is  therefore  a  base.  As  there  is  no  OH  in  Na2CO3,  the  nec- 
essary hydroxyl  ions  must  come  from  the  water  in  which  the 
carbonate  is  dissolved.  So  the  reaction  between  the  solvent, 
water,  and  the  Na2CO3,  the  solute,  is  represented  thus : 

2  Na+  •  CO3~  +  2  (H+  •  OH-)  ^  2  (Na+  •  OH')  +  H2CO3.    As 
NaOH  is  highly  dissociated,  this  then  is  the  source  of  the 
hydroxyl  ions.     A  solution  of  ferric   chloride  is  acid  in  re- 
action, and  similarly  this  is  accounted  for  by  the  following 
reaction:     Fe+++  -  3  Cl~    +3  (H+  •  OH~)  ^±  Fe(OH)3    + 

3  (H+  •  Cl~).     The  HC1  is  highly  dissociated  as  it  is  a  strong 
acid  and  yields  hydrogen  ions.     It  is  to  the  presence  of  these 
that  the  acid  character  is  attributed. 

Dissociation  of  Water.  —  We  have  seen  that  pure  water  is 
one  of  the  best  of  insulators  ;  consequently,  its  electrical  con- 
ductance is  very  slight.  This  conductance  must  be  due  to 
the  presence  of  hydrogen  and  hydroxyl  ions,  but  since  their 
ionic  conductances  are  the  greatest  of  any  ions  there  must 
be  but  a  few  of  them  to  account  for  the  slight  conductance 
of  pure  water.  Kohlrausch  found,  for  the  purest  water  that 
he  could  prepare,  a  conductance  at  18°  of  0.040  X  io~6. 

386 


HYDROLYSIS  387 

The  conductance  at  25°  C.  is  0.054  X  io~6.  From  the  con- 
ductance the  concentrations  of  the  hydrogen  and  of  the 
hydroxyl  ions  have  been  calculated,  and  it  is  found  to  be 
about  i.o  X  io~7  normal.  Or  applying  the  Mass  Law  to  the 
dissociation  of  water  we  have 

H2O  :£  H+  •  OH 

fc[H20]  =  [H+]  .  [OH-]. 

Solving  for  k,  the  dissociation  constant,  we  have 

fc_[H+]  -[OH-]. 
[H»0] 

but  since  the  concentration  of  the  undissociated  water, 
[H2O],  is  very  large  as  compared  to  the  dissociated  part, 
it  may  be  considered  as  practically  constant  and  the  equa- 
tion written  Kw  =  [H+]  •  [OH-].  Substituting  the  above 
value  of  the  concentrations  of  H+  and  OH~ ,  we  have 

Kw  =  [i.o  X  io-7]  •  [i.o  X  io-7]  =  i.o  X  io~14 

as  the  Ionic  Product  or  so-called  Dissociation  Constant 
of  water.  In  Table  LVIIIwe  have  compiled  the  Dissocia- 
tion Constant  of  a  few  acids  and  bases,  and  the  value  for 
water  is  very  small  as  compared  with  most  of  these. 

There  are  a  number  of  other  methods  by  which  the  disso- 
ciation of  water  has  been  determined,  and  among  these  may 
be  mentioned  the  Catalysis  of  Esters,  Catalytic  Muta-Rota- 
tion  of  Glucose,  Hydrolysis  of  Salts,  and  the  Electromotive 
Force  Method.  These  methods,  some  of  which  will  be  con- 
sidered subsequently,  give  results  that  compare  very  favor- 
ably with  the  above. 

The  change  in  temperature  affects  the  degree  of  dissocia- 
tion to  a  marked  extent,  as  the  data  in  Table  LXV  obtained 
by  Heydweiller  shows : 


388 


PHYSICAL   CHEMISTRY 


TABLE  LXV 
DISSOCIATION  CONSTANT  FOR  WATER 


t°C. 

0° 

10° 

1  8° 

25° 

50° 

100° 

150° 

218° 

Kw  X  io14 

0.116 

0.281 

0-59 

I.O4 

5-66 

58.2 

269 

630.1 

When  a  salt  is  dissolved  in  water  with  the  concomitant 
formation  of  free  hydrogen  or  hydroxyl  ions  through  the 
reaction  of  the  salt  with  the  water,  we  may  have  several  cases, 
depending  upon  the  ease  with  which  the  resulting  products 
of  the  reaction  are  ionized.  If  the  dissociation  constant 
of  the  acid  produced  is  greater  than  that  of  water,  the  solu- 
tion will  have  an  acid  reaction  ;  while  if  the  dissociation  con- 
stant of  the  base  is  greater  than  that  of  the  water,  the  solu- 
tion manifests  an  alkaline  reaction.  But  should  the  base  and 
acid  be  practically  un-ionized,  the  solution  will  be  neutral, 
and  we  have  the  case  of  the  formation  of  a  weak  acid  and  a 
weak  base  or  the  reverse,  while  in  the  former  case  we  have 
either  one  of  the  two  constituents  a  strong  electrolyte. 

As  an  example  of  the  case  when  one  of  the  two  products  of 
hydrolysis  is  a  strong  electrolyte,  we  may  select  acetanilid 
hydrochloride,  CeHgNt^QHsOCl.  The  ionic  reaction  is 
represented  thus  : 


C6H5NH2C2H30+  •  Cl-  +  HOH 


Applying  the  Mass  Law  we  then  have 
•  [C1-]  •  [HOH] 


H 


[H+]  -  [Cl-]. 


Since  this  is  a  dilute  solution,  the  concentration  of  the  water 
is  constant  and  the  concentration  of  the  chlorine  ions  ob- 


HYDROLYSIS  389 

tained  from  the  completely  dissociated  salt  is  the  same  as 
that  from  the  completely  dissociated  HC1,  hence  our  equa- 
tion may  be  written 

..          .       [CJfrNH,C.H.OOH]  •  [H+l 
Kk=  [C6H6NH2C2H30-] 

in  which  Kh  is  termed  the  Hydrolytic  Constant. 

The  dissociation  constant  of  water  is  Kw  =  [H+]  •  [OH~], 
from  which  the  concentration  of  the  hydrogen  ions  is 

rjr+1  = 


[OH-] 
The  dissociation  constant  for  the  base  is 

„   ,      [C6H6NH2C2H30+  ]  •  [OH- 


[C6H5NH2C2H3OOH] 

Substituting  the  value  of  the  hydrogen  ion,  [H+],  in  the  above 
equation  we  have 

K   . 
* 


[C6H6NH2C2H3O+]  •  [OH-] 

but  the  terms  in  brackets  are  —  •     Therefore,  substituting, 

Kb 

\  ~K 

we  have  Kh  =  —  -  ,  in  which    Kh  is  the  Hydrolytic  Constant 

Kb 

of  the  salt.    Kw  is  the  Ionic  Product  of  the  water  ;   Kb  is  the 
Dissociation  Constant  of  the  base. 

Similarly  by  selecting  a  salt  such  as  KCN,  which  on  hy- 
drolysis gives  an  alkaline  reaction,  it  may  be  readily  shown 

7V- 

that  the  hydrolytic  constant  Kh  =  —  -• 

Ka 

If  we  have  the  two  products  of  hydrolysis  both  weak  elec- 
trolytes, as  in  the  case  of  aniline  acetate,  C6HBNH3CH3COO, 
the  hydrolytic  constant  may  be  worked  out  in  a  similar 
manner. 


3QO  PHYSICAL  CHEMISTRY 

The  ionic  reaction  is  as  follows : 

C6H5NH3+  •  CHaCOO-  +  HOH 

$  C6H5NH3  •  OH  +  CHaCOOH. 

Applying  the  Mass  Law  Equation  we  have 

£[C6H5NH3+]  •  [CHaCOO-]  •  [HOH] 

=  [C6H6NH3OH]  •  [CHaCOOH] 

and  since  this  is  a  dilute  solution  the  concentration  of  the 
water  [HOK]  is  constant  and  the  products  of  the  hydrolytic 
dissociation  are  assumed  to  be  un-ionized,  the  equation  be- 
comes 

[C6H6NH3OH]  •  [CHaCOOH] 

[C6H6NH+3]  •  [CH3COO-] 
The  dissociation  constant  for  the  acid  is 

[CH3COO-]  •  [H+] 

[CH3COOH] 
therefore, 

[H+]  _  [CH3COOH] 
Ka   "    rCH3COO-] 

and  similarly  from  the  dissociation  constant  of  the  base  we 

have 

[OH-]  =  [C6H5NH3OH] 

Kb  [C6H5NH3+] 

Now  substituting  these  values  in  the  equation  above  we 

have 

K     _  [H+]  •  [OH-] 

K.-K, 

but  the  numerator  is  the  dissociation  constant  of  water,  Kw, 
hence  substituting  we  have 

"  w 


HYDROLYSIS  391 

which  is  the  kydrolytic  constant  for  the  cases  where  both  prod- 
ucts of  the  hydrolysis  are  weak  electrolytes. 

Degree  of  Hydrolysis.  —  The  Mass  Law  Equation  for  acet- 
anilid  hydrochloride  gives  us  the  hydrolytic  dissociation 
constant  according  to  the  equation 

[C6H5NH2C2H300H]  •  [H+] 


Now  if  x  is  the  degree  of  hydrolysis,  then  as  we  have  pre- 
viously seen  in  the  case  of  electrolytic  dissociation,  the  con- 
centrations of  the  ions  when  there  is  one  mole  of  the  salt 
dissolved  in  v  liters  of  water  are 

1  ~  x  mole  of  CeHsNHkQjHaO-  ions  unhydrolyzed 

-  mole  of  H+  ions 

v 

-  mole  of  C6H5NH2C2H3OOH  undissociated  base. 
v 

Substituting  these  values  in  the  equation,  we  have 
x     x 

TS  V         V         t.   ,        .  7,  x2 

Kh  =  -  which  gives  Kh  =  -,  -  —  • 
i  -  x  (i  -  x)v 

v 
Similarly  in  the  case  of  aniline  acetate  we  have  from 

K     =  [C6H5NH3OH]  •  [CH3COOH1 
[C6H6NH3+]  •  [CH3COO-] 

the  expression  for  the  hydrolytic  dissociation  the  equation 


Kh  = 


%  m  x 

V        V 


i  -  *vi  -  x\ 

v     )(     v     ) 


392  PHYSICAL  CHEMISTRY 

which  becomes 

as  the  hydrolytic  constant  for  the  cases  where  the  two  products 
of  hydrolysis  are  weak  electrolytes.  It  is  evident,  since  the 
term  for  the  volume  of  the  solution  does  not  appear  in  this 
equation,  that  in  cases  of  this  type  the  hydrolytic  dissocia- 
tion is  independent  of  the  volume. 

The  value  of  x,  the  degree  of  hydrolysis,  can  be  obtained 
experimentally  from  the  speed  of  inversion  of  cane  sugar  or 
the  hydrolysis  of  esters,  which  will  be  discussed  subsequently. 
Then  from  this  value  the  hydrolytic  constant  can  be  cal- 
culated from  the  equations  given  above. 

The  value  of  oo  is  determined  from  the  electrical  conduct- 
ance of  the  solutions  on  the  assumption  that  the  conductivity 
is  an  additive  property,  and  hence  the  conductance  of  the 
solution  is  the  sum  of  the  individual  conductances  of  the  ions 
present.  For  example,  in  the  case  of  acetaniline  hydrochlo- 

ride  we  have 

A  =  (i  —  x)A.v  +  #AHci, 

in  which  the  total  conductance,  A,  is  the  sum  of  the  conduct- 
ances of  the  un-hydrolyzed  salt  plus  the  conductance  of  the 
hydrochloric  acid.  Solving  for  x,  we  have 

A  -  Av 
x  = 


AHCI  —  Av 

As  the  HC1  is  completely  dissociated,  the  value  of  AHCL  be- 
comes its  value  A^ ,  and  the  value  Av  is  the  value  of  the  con- 
ductance of  the  salt  at  the  specified  volume,  assuming  no 
hydrolysis.  This  value  is  obtained  by  forcing  back  the 
hydrolysis  by  the  addition  of  a  large  excess  of  the  salt,  when 
Av  becomes  the  conductance  of  the  solution  A. 

In  Table  LXVI  will  be  found  the  values  for  the  degree  of 
hydrolysis  and  the  Hydrolytic  Constant  Kh  of  a  number 
of  compounds. 


HYDROLYSIS 
TABLE  LXVI 


393 


SUBSTANCE 

TEMP. 
C. 

CONCENTRA- 
TION LITERS 

PER    I   GM. 

EQUIV. 

METHOD 

PER  CENT 
HY- 
DROLYSIS 

HYDROLYSIS 
CONSTANT 

Acetanilid  hydrochloride     . 
Acetanilid  hydrochloride     . 
Acetanilid  hydrochloride     . 
Acetamid  hydrochloride 

25° 
40.2 

25 

32 

IO 

20 

IO 

Catalysis 
Catalysis 

"atalysis 

93-8 
98 

19 

Acetoxime  hydrochloride     . 
Aluminium  chloride    .     .     . 

'I 

IO 

Catalysis 
Inversion 

36 
4.72 

Aluminium  chloride    .     .     . 

64 

6.90 

Aluminium  chloride    .     .     . 

128 

8.49 

Aluminium  chloride    .     .     . 

256 

14.4 

Aniline  acetate  

25 

39-32 

Cond. 

Si-3 

Aniline  acetate  

40 

39.32 

59-o 

Ammonium  acetate    .... 

too 

40.13 

Cond. 

4.61 

Ammonium  bicarbonate      .     . 

25 

2.4  X  io-« 

Ammonium  chloride  .... 

25 

2-32 

O.OII 

3.1  X  lo-w 

Ammonium  chloride  .... 

18 

IOO 

Indirect 

O.O2 

Ammonium  chloride  .... 

218 

IOO 

1.6 

Ammonium  chloride  .... 

306 

IOO 

4.1 

Ammonium  citrate     .... 

IOO 

5 

3-86 

Ammonium  succinate      .     .     . 

100 

5 

Partial  Press. 

1-34 

IO 

Partial  Press. 

24.4 

Bismuth  chloride   

25 

0-4 

4.0 

50 

0.18-3.7 

3-1 

Br2  +  HOH  H+Br  +  HBrO  . 

25 

Dond. 

5-2  X  io-» 

Carbonic  acid    

25 

10 

Catalysis 

3-17 

Cerium  chloride     

IOO 

IO 

0.3 

C12  +  H20    H*C1-  +  HC1O    . 

0 

1.56  X  10  -•» 

C12  +  H2O    

15 

3.16  X  io-< 

C12  +  H20    

25 

4.48  X  10  -< 

Cb  +  H2O    

39.1 

6.86  X  10  -< 

Q2  _|_  JJ2O 

e->  6 

9.01  X  io"4 

CI2  +  H20    

ot.6 

10.36  X  10  -< 

C12  +  H2O    

83.4 

10.93  X  lo-4 

Sodium  Salt  of  Chlorphenol      . 

25 

10 

Catalysis 

1.62 

2  •  4  Dichlorphenol       .     . 

25 

10 

Catalysis 

0.29 

2.4-6  Trichlorphenol 

25 

10 

Catalysis 

0.21 

p  Cyanphenol        

2  e 

IO 

Catalysis 

O  2O 

Ferric  chloride  

^  j 

25 

6.67 

Cond. 

u.^y 
2 

Ferric  chloride  

33.34 

37 

Ferric  chloride  

333-4 

84 

Ferric  chloride  

666.7 

91 

Glycocoll  hydrochloride       .     . 
Glycocoll  hydrochloride  .     .     . 

25 
25 

10 
IO 

Catalysis 
[aversion 

3 

Sodium  cyanate               .     . 

or 

IO 

Catalysis 

I.I  2 

Lanthanum  chloride  .... 

*0 
IOO 

IO 

Inversion 

o-3 

Nickel  chloride  

2  e 

AA—IC    2 

Inversion 

O  7O 

0.3    X  10  -« 

Nickel  sulphate      

^j 
2  e 

4^4 

Inversion 

u.^v 
?2-  OAA 

i.i    X  10  -" 

Potassium  cyanide      .... 

10.3 

H-^""+ 

9.63 

Inversion 

34    >W^H+ 

1.48 

Potassium  cyanide      .... 
Potassium  cyanide      .... 

25-05 
41.8 

9.63 
9-63 

Inversion 

1.73 
1.98 

Potassium  cyanide      .... 

42.5 

9.63 

2.  II 

Propionitrile  hydrochloride 
Propionitrile  hydrochloride 
Sodium  bicarbonate    .... 

25 
25 

18 

10 
IO 
I-IOOO 

Catalysis 
Inversion 

99 

92 

i.S    Xio-« 

Sodium  bicarbonate    .... 

25 

I-IOOO 

2.5    X  10  •« 

Sodium  carbonate  

25 

5 

i-3 

1.9    X  io-4 

Sodium  carbonate  

25 

IO 

2-9 

Sodium  carbonate  

25 

20 

4-5 

394 


PHYSICAL   CHEMISTRY 


TABLE  LXVI  —  Cont. 


SUBSTANCE 

TEMP. 
C. 

CONCENTRA- 
TION LITERS 

PER    I   GM. 

METHOD 

PER  CENT 
HY- 

HYDROLYSIS 

CONSTANT 

EQUIV. 

DROLYSIS 

Sodium  carbonate  ... 

25 

100 

"•3 

Sodium  carbonate  ... 

25 

200 

16.0 

Sodium  carbonate  ... 

25 

IOOO 

34-0 

Urea  hydrochloride     .     . 
Urea  hydrochloride     .     . 

25 
25 

IO 
10 

Catalysis 
Inversion 

90 

81 

Thiourea  hydrochloride  . 
Thiourea  hydrochloride 

25 

10 

Catalysis 
Inversion 

99 

92 

o-Toluidine  hydrochloride 

25 

10 

Inversion 

3-2 

o-Toluidine  hydrochloride 
p-Toluidine  hydrochloride 

25 
25 

10 
10 

Conductivity 
Inversion 

1.8 
i-7 

p-Toluidine  hydrochloride 

25 

10 

Conductivity 

0.9 

CHAPTER  XXXIII 
NON AQUEOUS   SOLUTIONS 

IN  our  study  of  solutions  we  have  been  considering  pri- 
marily aqueous  solutions,  and  the  numerous  theories  we  have 
been  studying  have  been  developed  from  these.  The  ques- 
tion arises,  Are  these  theories  applicable  to  solutions  wherein 
any  substance  may  be  taken  as  the  solvent,  or  are  they  only 
applicable  to  the  solutions  in  which  water  is  the  solvent? 
We  have  just  considered  in  detail  the  Electrolytic  Theory 
of  Dissociation  as  developed  to  explain  certain  abnormal 
values  obtained  in  aqueous  solutions  wherein  the  solute 
was  assumed  to  be  independent  of  the  solvent  and  was  dis- 
sociated by  it.  Then  we  saw  that  many  facts  have  been  col- 
lected that  are  now  being  explained  upon  the  basis  of  a  com- 
bination of  the  solvent  and  the  solute  as  well  as  a  combina- 
tion of  the  dissociated  parts  of  the  solute  with  the  solvent. 
Particularly  in  concentrated  solutions  have  these  assumptions 
of  hydration  been  made  to  account  for  the  abnormal  values 
presented  by  the  data  collected  and  interpreted  in  the  light 
of  the  theory  of  dilute  solutions. 

The  question  arises,  Can  we  employ  these  methods  to  the 
determination  of  the  various  properties  of  nonaqueous 
solutions,  and  can  the  data  collected  by  them  be  interpreted 
in  a  similar  manner  ?  For  example,  do  nonaqueous  solvents 
yield  solutions  that  conduct  the  electric  current,  and  does  the 
conductance  represent  the  degree  of  dissociation  of  the 
solute  ?  Is  an  electrolyte  dissociated  to  the  same  extent  by 
all  solvents  ;  do  the  ions  have  the  same  ionic  conductance  in 
different  solvents,  —  if  they  do  not,  why  not,  —  or  in  other 

395 


3Q6  PHYSICAL   CHEMISTRY 

words,  to  what  is  the  ionization  of  the  solute  due  ?  We  know 
that  some  solvents  yield  conducting  solutions,  while  others 
do  not.  Then  is  the  degree  of  dissociation  as  determined  by 
the  conductivity  comparable  to  that  determined  by  the  other 
methods  that  are  employed  in  aqueous  solutions,  such  as 
freezing  point,  boiling  point,  osmotic  pressure,  and  vapor 
pressure  ?  It  is  therefore  evident  that  the  detailed  considera- 
tion of  nonaqueous  solutions  requires  an  extensive  study  of 
the  methods  and  theories  we  have  been  considering,  as  applied 
to  solutions  of  solvents  other  than  water.  During  the  last 
few  years  many  investigators  have  collected  an  enormous 
amount  of  data  and  have  attempted  to  correlate  these  in  the 
light  of  the  theories  developed  on  the  basis  of  aqueous  solu- 
tions. 

One  of  the  principal  questions  that  has  been  discussed  is, 
To  what  is  the  ionizing  power  of  a  solvent  due?  Various 
explanations  have  been  presented,  and  we  shall  take  up  a 
consideration  of  these  in  our  presentation.  Among  these 
may  be  mentioned  the  relation  between  the  ionization  power 
of  the  solvent  and  its  dielectric  constant,  its  association  fac- 
tor, the  electrical  conductance  of  its  solutions,  the  viscosity, 
the  combination  of  the  solvent  and  solute,  as  well  as  the  low- 
ering of  the  freezing  point,  the  rise  of  the  boiling  point,  and 
the  osmotic  pressure  of  the  solutions. 

Electrical  Conductance.  —  Determinations  of  the  electri- 
cal conductances  of  solutions  of  many  solvents,  both  organic 
and  inorganic,  have  been  made.  These  show  that,  as  in  the 
case  of  water,  the  conductance  of  the  pure  solvent  is  very 
small,  while  the  solutions  have  a  very  appreciable  conduct- 
ance. In  most  cases  the  conductance  is  less  than  in  aqueous 
solutions,  but  in  a  few  cases  they  conduct  much  better. 
Such  inorganic  solvents  as  NH3,  SO2,  and  HCN  yield  solu- 
tions that  conduct  very  well,  in  many  cases  as  well  as  water 
solutions,  while  the  solutions  of  various  solutes  in  PC13,  AsCl3, 
etc.,  have  a  relatively  small  conductance.  A  consideration  of 


NONAQUEOUS   SOLUTIONS 


397 


the  various  groups  of  organic  solvents  shows,  in  a  general  way, 
that  liquid  hydrocarbon  solutions,  as  well  as  their  halogen 
substitution  products,  are  nonconductors.  The  alcohols 
yield  solutions  that  conduct  very  well,  but  the  conductance 
decreases  with  the  increase  of  the  carbon  content  as  well  as 
with  the  complexity  of  the  alcohol.  The  aldehydes  yield 
conducting  solutions,  and  many  of  the  solutions  of  ketones 
are  excellent  conductors,  while  the  esters  yield  conducting 
solutions  which  are  however  not  very  good  conductors. 
Many  of  the  organic  compounds  containing  nitrogen,  such  as 
the  organic  bases,  amines,  and  nitriles,  yield  solutions  that 
conduct ;  the  nitriles  in  particular  yield  solutions  that  are 
excellent  conductors. 

The  conductance  of  alcoholic  solutions,  particularly  methyl 
and  ethyl  alcohols,  has  been  studied  extensively,  and  in 
general  limiting  values  of  the  conductance  have  been  found. 
From  these  values,  then,  as  in  the  case  of  aqueous  solutions, 
the  degree  of  dissociation  of  the  solute  has  been  calculated.  In 
Table  LXVII  are  given  Carrara's  values  for  A^  for  a  number 
of  solutes  in  methyl  alcohol  solutions.  Some  of  these  may  be 
readily  compared  with  the  values  in  aqueous  solution  Table 
L.  These  values  of  A^  are  expressed  in  the  reciprocal 
Siemens  unit. 

TABLE  LXVII 
A^  IN  METHYL  ALCOHOL 


CL 

BR 

I 

OH 

H 

T  -I  7    «O 

I  "\A.  ^ 

Li 

iOO't"-' 

77  1 

Na      

K                                 .          .  ••', 

86.80 
QC  cy 

87.58 
06  ^2 

89.77 

Q7.6"; 

71.83 

75.75 

NH4  

06.24. 

QQ.QT. 

IOS-25 

(82.00) 

TSJ/p-LT    \ 

IN  lwHsJ4         

N(dHi)4     

06  76 

96.62 

ii5-3° 
113.76 

91.1^ 

S(CH3)3       .     .     .     .    ^    .     . 

1  00.09 

102.5 

116.38 

97-34 

\ 


398 


PHYSICAL   CHEMISTRY 


Since  the  value  of  A^  depends  on  the  ionic  conductances, 
Carrara  has  calculated  these  values  for  a  number  of  the  ions, 
and  these  are  given  in  Table  LXVIII.  To  compare  these 
values  with  the  values  given  for  aqueous  solutions  in  Table 
LII,  they  will  have  to  be  converted  to  mhos. 

TABLE  LXVIII 
EQUIVALENT  IONIC  CONDUCTANCE  IN  METHYL  ALCOHOL 


CL 

BR 

I 

Li                    * 

27  8 

Na  
K 

37-3 
4.6  i 

37-3 

4.6  T> 

37-3 

AC    2 

NH4     

46  8 

40  5 

^  8 

N(CH3)4    

63.1 

N(C2H5)4 

46  ^ 

4.6  4. 

61  ^ 

S(CH3)2     

SI.  4 

40  q 

64.  o 

H 

8*  * 

82  c 

OH  ...... 

T>2  O 

Cl    .     . 

4.0  c 

Br    .     .     .     . 

KO  2 

I       

c.2.4 

CH3COO 

•z-i  o 

CC13COO  .... 

•16  O 

With  few  other  solvents  has  the  work  been  so  extensive 
as  with  the  alcohols,  but  it  is  found  that  in  most  cases  the 
limiting  values  of  the  equivalent  conductance,  A^ ,  cannot  be 
obtained  experimentally,  and  neither  have  the  ionic  conduct- 
ances been  ascertained.  We  have  therefore  too  meager  data 
in  most  cases  for  the  calculation  of  the  degree  of  dissociation 
of  the  solute  from  the  conductances  of  the  solutions.  The 
marked  conductance  of  certain  solutions  of  nonaqueous  sol- 
vents is  accounted  for  on  the  basis  that  although  the  degree 
of  dissociation  is  less  than  in  aqueous  solutions  the  speed  of 
migration  of  the  ions  is  much  greater  than  in  water,  and  con- 


NONAQUEOUS   SOLUTIONS  399 

sequently  the  conductance  is  greater.  In  such  solvents  as 
hydrocyanic  acid,  ammonia,  pyridine,  and  some  nitriles, 
the  conductance  of  solutions  of  certain  electrolytes  is  much 
greater  than  their  aqueous  solutions.  The  equivalent  con- 
ductance increases  with  the  dilution,  but  there  are  a  few 
marked  exceptions.  In  pyridine  and  benzaldehyde  solu- 
tions the  equivalent  conductance  of  ferric  chloride  decreases 
with  the  dilution.  This  was  also  found  to  be  the  case  in  solu- 
tions of  HC1  in  ether  and  also  in  isoamyl  alcohol,  as  well  as  in 
solutions  of  sulphuric  acid ;  and  in  acetic  acid  the  molecular 
conductance  decreased  with  the  increased  dilution.  Dutoit 
and  Friderich  found  the  conductance  of  CdI2  to  be  practically 
constant  with  the  change  of  dilution  in  acetophenone  solu- 
tions, and  in  methly  propyl  ketone  and  methyl  ethyl  ketone 
the  equivalent  conductance  decreases  with  the  dilution. 
This  is  also  true  of  stannous  chloride  in  acetone.  Euler  found 
the  molecular  conductance  of  both  Nal  and  NaBr  in  benzo- 
nitrile  to  decrease  with  the  dilution  and  this  is  also  true  of 
solutions  of  silver  nitrate  in  piperidine. 

Dielectric  Constant.  —  It  will  be  recalled  that  the  elec- 
trostatic action  of  two  electrically  charged  bodies  varies  with 
the  nature  of  the  medium  in  which  they  are  placed.  A  sub- 
stance which  is  a  very  poor  conductor,  or  is,  as  we  say,  an  in- 
sulator, is  also  called  a  dielectric.  Upon  ionization  of  a  solute 
in  a  nonconducting  solvent,  the  charged  ions  will  be  sepa- 
rated by  this  medium,  and  Faraday  emphasized  that  its 
nature  must  be  taken  into  consideration.  This  is  always 
constant  for  a  given  medium  and  is  termed  the  specific  induc- 
tive capacity  and  is  familiarly  known  as  the  Dielectric  Con- 
stant. Thomson,  and  subsequently  Nernst,  emphasized 
the  relation  between  the  dissociative  or  ionizing  power  of  a 
solvent  and  its  dielectric  constant.  They  showed  that  the 
greater  the  dielectric  constant  the  greater  the  ionizing  power 
of  the  solvent,  and  this  is  known  as  the  Thomson-Nernst 
Rule. 


400 


PHYSICAL   CHEMISTRY 
TABLE  LXIX 


SOLVENT 

COEFFI- 
CIENT 

OF 

ASSOCI- 
ATION 

CJ 

a 
fi 

DIELEC- 
TRIC 
CON- 
STANT 
AIR  =  I 

U 
t 

VISCOS- 
ITY TJ 

SOLUTE 

V 

A 

Hexane  

17 

1.88 

20 

0.0033 

Amylene      .... 

0.96 

15.8 

2.20 

Benzene  

I.OI 

18 

2-3 

20 

0.0064 

Toluene 



TO 

c 

c 

Chloroform      .     .     . 

0.94 

17 

4-95 

20 

0.0054 
0.0057 

Ethylene  chloride      . 

20 

10.4 

20 

0.0084 

Acetyl  chloride     .     . 

i.  06 

20 

15-5 

Methyl  alcohol     .     . 

3-43 

18 

31-0 

20 

0.0060 

KI 

00 

97-6 

NfC2H5)4l 

00 

124 

Ethyl  alcohol  .     .    T 

2-74 

20 

25.8 

20 

0.0119 

KI 

5000 

47-8 

N(C2Hs)4l 

00 

60 

Allyl  alcohol    .     .     . 

1.88 

21 

20.6 

20 

0.0136 

Nal 

813.4 

33-1 

NaCl 

1066.6 

33-1 

Propyl  alcohol      .     . 
Benzyl  alcohol      .     . 

2.25 

21 

22.2 
IO.6 

20 
20 

0.0225 
0.0558 

SrI2 
FeCls 

128 

895.2 

10.2 

6.3 

Epichlorhydrine    .     . 

— 

2O 

23-0 

N(C2H5)4l 

00 

66.8 

Phenol    

1.42 

48 

9.68 

45 

0.040 

Ethyl  ether      .     .     . 

0.99 

18 

4-35 

20 

0.00226 

' 

Acetic  aldehyde    .     . 
Paraldehyde     .     .     . 
Benzaldehyde  .     .     . 

0.85 
0.97 

20 
20 
20 

14.8 
n.8 
18.0 

19.2 

0.00233 

FeCls 
FeCls 

183.1 
237-1 

16.5 
10.5 

N(C2H5)4l 

00 

43 

Acetone  

1.26 

20 

21.5 

19 

0.0033 

AgNOs 

576 

16.5 

N(C2H5)4l 

00 

225 

Methyl  propyl  ketone 
Methyl  ethyl  ketone 

l.n 

17 
17 

^7-8 

20 
20 

0.005 
0.0044 

FeCls 
CHS  -  NH4 

1074 
94.8 

59-5 
19.7 

Acetophenone  .     .     . 

1.  10 

20 

18.1 

FeCls 

293 

13-1 

Ethyl  acetate  .     .     . 

0.99 

20 

5-85 

20 

0.00451 

FeCls 

67.6 

Ethyl  cyan  acetate   . 

20 

27.7 

FeCls 

185.2 

11^6 

Ethyl  acetoacetate    . 

0.96 

22 

iS-7 

20 

0.0191 

FeCls 

503.5 

23.4 

Ethyl  benzoate     .     . 

— 

19 

6.04 

20 

0.0067 

FeCls 

517-2 

1.91 

Nitrobenzene  .     .     . 

1-13 

18 

36.45 

25 

0.0183 

FeCls 

2904 

20.5 

N(C2H5)4l 

OO 

40.0 

Aniline    

1.05 

18 

7-32 

2O 

.0.0447 

Pyridine      .... 

0-93 

21 

12.4 

25 

0.0089 

AgNOs 

140.7 

36-2 

NH4I 

2528.6 

41.0 

Piperidine    .     .     .     „" 

i.  08 

20 

5-8 

AgNOs 

4.24 

o.37 

Quinoline     .... 
Phenyl  hydrazine 

0.81 

21 

23 

8.8 
7-i5 

AgNOs 

129.9 

3-62 

Acetonitrile      .     .     . 

1.67 

20 

58.8 

0.0033 

AgNOs 

128 

IT8.3 

N(C2H5)4I 

00 

200 

Propionitrile     .     .     . 

i-77 

20 

27-7 

0.0040 

AgNOs 

256 

38.9 

N(C2H5)4l 

00 

165 

Butyronitrile  .     .     . 
Benzonitrile     .     .     . 

1.22 
1.  00 

21 
20 

20.3 
26.5 

0.0056 

AgNO' 
AgNOs 

150 
803 

32.1 

21.6 

N(C2H5)4I 

00 

56.5 

Inorganic  Solvents 

NHs   

-50° 

22.7 

AgNOs 

251.4 

195-2 

Orthonitrophenol 

2000 

10.3 

SOa    

20° 

14.0 

KI 

2048 

126.0 

N(C2H5)4l 

1024 

154-7 

HCN      

21° 

95 

KI 

1024 

308 

Orthonitrophenol 

2299 

148.3 

AsCla 

17° 

3-6 

PCls 

I.  O2 

22° 

4-7 

H?O    

18° 

81.1 

2O 

0.01006 

AgNOs 

00 
00 

1  15.8 
131-1 

NONAQUEOUS  SOLUTIONS  401 

In  Table  LXIX  will  be  found  the  dielectric  constants  for  a 
large  number  of  types  of  solvents.  It  has  been  found  that 
in  general  the  Thomson-Nernst  rule  does  hold,  and  those 
solvents  with  the  highest  dielectric  constants  yield  the  best 
conducting  solutions.  The  conductance  of  the  solution  is, 
however,  not  commensurate  with  the  dielectric  constant,  as 
is  shown  by  an  examination  of  the  columns  containing  the 
data  of  the  conductances  of  a  number  of  solutes  in  various 
solvents.  Some  of  the  most  conspicuous  exceptions  to  the 
rule  are  given  in  the  Table.  In  addition  to  these  it  may  be 
mentioned  that  the  value  for  LiCl  in  water  of  A^  at  1 8°  is  95, 
and  that  at  dilution  of  3000  liters  in  propyl  alcohol  is  1 28.9  ;  in 
fact,  most  of  the  values  for  propyl  alcohol  solutions  (D.C.  2 1 .6) 
are  greater  than  those  for  solutions  in  water  (D.C.  81).  The 
values  of  A  for  acetonitrile  (D.C.  38.8)  solutions  approximate 
closely  those  of  many  of  the  solutes  in  water.  The  value 
of  A  for  Nal,  NH4I,  N(C2H5)4l  and  of  S(C2H5)I  in  acetone 
(D.C.  2 1 .5) ,  according  to  Carrara,  is  greater  in  dilute  solutions 
than  the  assigned  values  of  A^  in  aqueous  solutions.  In  the 
case  of  hydrocyanic  acid  solutions  the  dielectric  constant  (95) 
indicates  that  we  should  have  excellent  conducting  solutions, 
but  as  a  matter  of  fact  they  are  comparatively  poor  conductors 
as  compared  with  aqueous  solutions.  Orthonitrophenol  forms 
solutions  that  conduct  poorly  as  compared  with  solutions  of 
the  same  solute  in  ammonia.  In  general,  however,  ammonia 
solutions  are  better  conducting  solutions  than  the  correspond- 
ing aqueous  solutions .  Nitrobenzene  (D.C.  36.5)  yields  poor 
conducting  solutions,  the  conductivity  of  which  is  not  at  all 
commensurate  with  the  magnitude  of  its  dielectric  constant. 

The  increase  in  the  conductance  with  the  increased  tem- 
perature holds  generally,  as  in  the  case  of  aqueous  solutions, 
but  there  are  a  few  marked  exceptions.  The  conductance 
of  CdI2  in  acetonitrile  is  practically  the  same  over  the  range 
of  temperature  from  o.2°to37.2°C.,  and  in  acetone  the  tem- 
perature coefficient  is  virtually  zero. 


402  PHYSICAL   CHEMISTRY 

Association  Constant.  —  Dutoit  and  Friderich  from  the 
result  of  their  extensive  researches  on  nonaqueous  solutions 
concluded  that  only  in  associated  liquids  are  the  electrolytes 
dissociated,  and  the  more  highly  the  solvent  is  associated  the 
greater  is  its  ionizing  power  and  consequently  the  better  do 
its  solutions  conduct  the  electric  current.  In  Table  LXIX  are 
given  the  association  constants  of  a  number  of  solvents,  and 
while  in  general  the  solvents  that  yield  the  best  conducting  so- 
lutions are  polymerized,  the  reverse  is  not  true,  for  many  sol- 
vents that  are  not  supposed  to  consist  of  associated  mole- 
cules do  yield  solutions  that  conduct  the  electric  current. 
For  example,  water,  the  alcohols,  the  nitriles,  and  the  ketones 
are  the  most  highly  associated  liquids,  and  they  are  the 
solvents  that  yield  the  best  conducting  solutions.  The  alde- 
hydes, nitrobenzene,  benzonitrile,  and  the  esters  are  not  poly- 
merized liquids,  but  they  yield  solutions  that  conduct  the  elec- 
tric current,  and  many  of  them  are  fairly  good  conductors. 
Crompton  emphasized  the  connection  between  the  specific 
inductive  capacity  and  the  degree  of  association  of  the  sol- 
vents, and  Abegg  also  pointed  out  this  parallelism,  but  he 
also  observes  that  nitrobenzene,  ethyl  nitrite,  and  benzo- 
nitrile all  have  rather  high  dielectric  constants ;  yet  their 
association  factors  are  unity.  Crompton  states :  "  It  is 
almost  impossible  to  doubt  that  association  plays  an  all-im- 
portant part  in  determining  the  value  of  the  specific  inductive 
capacity  of  a  liquid  and  that  if  there  is  any  connection  be- 
tween the  specific  inductive  capacity  and  the  power  of  form- 
ing electrolytes,  it  may  be  looked  for  rather  in  the  fact  that 
electrolytes  are  solutions  of  approximately  monomolecular 
salts  in  an  associated  solvent  rather  than  in  there  being  any 
peculiar  '  dissociative  power  '  attached  to  the  solvent." 

Colligative  Properties.  —  Numerous  freezing  point  and 
boiling  point  determinations  of  nonaqueous  solutions  have 
been  recorded,  but  the  data  on  vapor  pressure  and  osmotic 
pressure  measurements  are  rather  meager. 


NONAQUEOUS   SOLUTIONS 


403 


The  degree  of  dissociation  as  calculated  from  boiling  point 
determinations  shows  closer  agreement  with  the  values  by  the 
conductivity  method  in  methyl  alcohol  solutions  than  in  the 
case  of  other  alcoholic  solutions.  In  Table  LXX  are  given 
the  comparative  values  of  the  degree  oT  dissociation  as  calcu- 
lated from  the  boiling  point  determinations  of  Woelfer  and 
the  conductivity  measurements  of  Vollmer. 

TABLE  LXX 


METHYL  ALCOHOL 

ETHYL  ALCOHOL 

Per  Cent  of 

a  by  the 

a  by  the 

Per  Cent 

a  by  the 

a.  by  the 

Solute 

Boiling  Pt. 

Conductivity 

of  Solute 

Boiling  Pt. 

Conductivity 

LiCl    .     . 

0-45 

0.63 

0-57 

0.9 

0-35 

0.32 

KI      .     . 

0.36 

0.61 

0.79 

0.78 

0.29 

0.49 

Nal     .     . 

0.44 

0.87 

0.74 

2.14 

0.27 

0-45 

Nal     .     . 

0.68 

0-51 

0.56 

AgN03     . 

0.533 

0.65 

0.38 

CHgCOOK 

0.48 

0.48 

0.63 

1.07 

0.18 

O.22 

CHsCOONa 

0.40 

0.49 

0.63 

0.97 

O.OI 

O.24 

It  must  be  remembered  that  these  sets  of  values  are  cal- 
culated from  data  at  different  temperatures.  At  the  temper- 
ature of  the  conductivity  measurements,  18°,  the  viscosity 
factor  for  ethyl  alcohol  is  about  0.01211,  while  at  the  boiling 
point  it  has  decreased  to  approximately  0.00521,  yet  there  is 
no  regularity  of  results. 

In  acetone  solutions  Dutoit  and  Friderich  found  normal 
values  for  the  molecular  weight  by  the  boiling  point  method, 
yet  these  solutes  yield  solutions  that  conduct.  LiCl  and  CdI2 
yield  solutions  that  conduct  fairly  well,  which  would  indicate 
that  they  are  quite  highly  dissociated,  but  the  boiling  point 
determinations  indicate  that  they  are  not  dissociated. 

In  benzonitrile  Werner  found  normal  molecular  weights 
for  AgNO3,  while  the  solutions  conduct  well,  showing  marked 
dissociation.  He  also  found  normal  molecular  weights  for 


404 


PHYSICAL   CHEMISTRY 


salts  of  the  heavy  metals  in  pyridine.  The  average  of  the 
values  for  AgNO3  is  165.4,  theory,  169.55  ;  for  Hg(CN)2, 
216.68,  theory,  251.76;  for  HgI2,  308.0,  theory,  452.88; 
and  for  Pb(NO3)2,  352.07,  theory  requires  330.35.  In  most 
cases  he  found  values  slightly  under  the  theoretical. 

From  these  data  it  is  apparent  that  there  is  not  that  agree- 
ment between  the  degree  of  dissociation  as  calculated  from 
the  boiling  point  or  the  cryoscopic  determinations  and  from 
the  conductivity  measurements  in  nonaqueous  solutions 
as  has  been  found  to  hold  in  aqueous  solutions,  and  this  has 
been  confirmed  by  numerous  investigators. 

Ostwald's  Dilution  Law.  —  We  have  already  seen  how  well 
this  Dilution  Law  of  Ostwald  holds  in  the  case  of  aqueous 
solutions,  and  many  attempts  have  been  made  to  apply  it  to 
nonaqueous  solutions.  Most  investigators,  including  Voll- 
mer,  Woelfer,  Cattaneo,  and  others,  have  found  that  Ost- 
wald's Dilution  Law  does  not  hold  for  methyl  and  ethyl 
alcoholic  solutions.  Cohen,  who  has  considered  this  subject 
at  considerable  length,  comes  to  the  same  conclusion.  The 
data  given  in  Table  LXXI  show  that  the  formulae  of 
Rudolphi  and  of  Ostwald  do  not  hold  when  applied  to 
alcoholic  solutions.  The  following  data  for  a  solution  of 
potassium  acetate  are  taken  from  Cohen's  results. 

TABLE  LXXI 


V 

A 

100  KR 

100  KO 

11.4 

8.28 

0.82 

0.242 

113.0 

I7.I8 

0-59 

0.055 

1  120.0 

27.00 

0.49 

0.014 

3520.0 

29.20 

0.36 

0.006 

The  value  of  the  constant  obtained  by  Rudolphi 's  formula, 
KR,  does  not  vary  nearly  so  much  as  that  obtained  from 
Ostwald's  formula,  KQ.  The  value  of  A^  is.  necessary  for 


NONAQUECUS   SOLUTIONS 


405 


the  calculation  of  these  constants,  and  we  have  seen  that 
the  data  for  this  are  very  meager,  and  not  sufficiently  exact, 
in  most  cases,  to  justify  its  use  in  this  connection,  and  par- 
ticularly is  this  true  in  those  cases  where  the  conductance 
decreases  with  the  dilution. 

Mixtures  of  Solvents.  —  Within  recent  years  the  problem 
of  the  conductance  of  electrolytes  in  mixtures  of  two  different 
solvents  has  been  the  subject  of  numerous  investigations. 
It  is  beyond  our  purpose  to  discuss  this  work  in  detail,  but  a 
few  illustrations  of  the  data  collected  will  indicate  some  of  the 
peculiarities  of  these  solutions. 

In  Table  LXXII  are  given  the  molecular  conductances  of 
certain  salts  in  aqueous  solutions,  A  ;  in  methyl  alcoholic  solu- 
tions, B  ;  and  in  50  per  cent  solutions  of  methyl  alcohol  and 
water,  C.  These  values  are  taken  from  the  work  of  ^elinsky 
and  Kraprivin,  and  expressed  in  the  reciprocal  Siemens  unit. 

TABLE  LXXII 


A  FOR  KBr 

A  FOR  NH4Br 

r 

A 

B 

C 

A 

B 

C 

16 

I23.I 

59.82 

127.2 

65-43 

61.16 

32 

127-5 

69.02 

62.46 

I3I.8 

72.73 

63.81 

64 

130.5 

76.70 

65.36 

135-3 

79.56 

66.04 

128 

132.9 

83.60 

67.11 

138.6 

85.80 

6745 

256 

136.4 

88.96 

69.26 

I4I.2 

90.88 

68.32 

512 

140.2 

93.26 

70-53 

143-5 

94-99 

69.10 

1024 

1434 

97-25 

145.6 

98.24 

70.11 

It  will  be  noticed  that  the  equivalent  conductance  of  the 
methyl  alcohol  solutions,  B,  is  less  than  that  of  the  aqueous 
solutions,  A,  and  that  of  the  mixtures,  C,  is  much  below  that 
of  the  methyl  alcohol  solutions.  These  minimum  values 
have  been  emphasized  by  several  workers,  including  Jones  and 
his  colaborers,  Cohen,  and  others.  In  other  cases  marked 


a 
406  PHYSICAL  CHEMISTRY 

maximum  values  are  found  in  solutions  of  other  salts  in  mix- 
tures of  solvents,  as  illustrated  in  the  case  of  lithium  nitrate 
in  mixtures  of  acetone  and  methyl  alcohol  and  of  silver  nitrate 
in  mixtures  of  ethyl  alcohol  and  acetone,  particularly  at  the 
higher  dilutions.  There  seems  to  be  some  parallelism  be- 
tween these  maximum  values  and  the  minimum  viscosity  of 
the  mixtures. 

Carrara  has  shown  that  the  electrolytic  dissociation  of 
water  in  methyl  alcohol  is  greater  than  in  aqueous  solutions, 
while  the  reverse  is  the  case  in  ethyl  alcohol.  It  is  also  of 
interest  to  note  that  KOH  and  NaOH  in  methyl  alcohol  show 
the  same  conductance  as  CH3OK  and  CH3ONa. 

Additional  Theories.  —  From  a  consideration  of  the  opti- 
cal properties  of  solvents,  Bruhl  comes  to  the  conclusion  that 
oxygen,  is  generally  tetravalent.  He  attributes  the  poly- 
merization of  the  molecules  of  water  and  of  other  oxygenated 
liquids,  their  high  specific  inductive  capacity,  as  well  as  the 
dissociative  power  exerted  upon  the  dissolved  substance,  to 
their  being  unsaturated  compounds.  It  is  true  that  a  great 
many  oxygenated  solvents  do  yield  solutions  that  conduct 
electricity;  but  it  has  been  pointed  out  by  Dutoit  and 
Friderich  that  the  ethers  and  the  ether  salts  are  not  poly- 
merized solvents,  and  that  they  yield  solutions  that  do  not 
conduct,  or  the  conductance  of  which  is  very  slight,  as  in  the 
case  of  ferric  chloride  solutions  in  phenyl-methyl  ether. 
Ethyl  carbonate  does  not  yield  solutions  that  conduct.  The 
same  is  true  for  chloral  solutions,  and  the  esters  of  high  car- 
bon content  yield  solutions  the  conductance  of  which  is  very 
slight.  In  the  case  of  the  substitution  of  chlorine  for  the 
ethoxy  group  in  ethyl  carbonate,  the  number  of  spare  valences 
is  undoubtedly  reduced,  yet  this  product,  ethyl  chlorcar- 
bonate,  yields  solutions  that  conduct  well. 

In  compounds  containing  nitrogen,  Bruhl  holds  that  the 
conductance  of  their  solutions  is  due  to  the  extra  valences  of 
the  nitrogen.  He  predicts  that  hydrazine  will  prove  to  yield 


NONAQUEOUS   SOLUTIONS  407 

solutions  that  conduct,  but  phenylhydrazine  does  not  yield 
solutions  of  the  salts  tested  that  conduct  electricity;  how- 
ever, it  still  remains  to  be  seen  what  hydrazine  will  do.  He 
states  that,  in  general,  the  dissociative  power  in  the  case 
of  nitrogen  compounds  will  vary  with  the  nitrogen  content, 
without  being  proportional  to  it,  however ;  just  as  he  claims 
that  it  varies  with  the  oxygen  content  of  oxygen  compounds. 
He  further  predicts  that  the  anhydrous  hydrocyanic  acid, 
diazo  compounds,  and  even  unsaturated  compounds  of  the 
elements  other  than  oxygen,  namely,  PC13,  AsCl3,  mercap- 
tans,  and  sulphur  ethers,  will  possess  dissociation  power. 
Attention  has  been  called  to  the  fact  that  when  the  CN  group 
is  substituted  for  hydrogen  in  ethyl  acetate,  the  equivalent 
conductance  is  materially  increased.  Hydrocyanic  acid 
and  nitriles  do  yield  solutions  that  conduct  very  well.  Con- 
trary to  Bruhl's  prediction,  PC13  does  not  yield  solutions  that 
conduct ;  but  in  the  case  of  AsCl3  his  prediction  is  confirmed. 
Werner  found  that  solutions  of  cuprous  chloride  in  methyl 
sulphide  conduct  very  poorly.  From  the  evidence  we  have 
at  present  it  seems  that  the  theory  that  the  dissociative  power 
of  solvents  is  due  to  the  unsaturated  valences,  that  is,  that 
the  only  solvents  that  yield  solutions  that  conduct  electricity 
are  unsaturated  compounds,  is  not  substantiated  by  the  facts 
in  many  cases.  Therefore  the  theory  as  promulgated  by 
Bruhl  is  untenable. 

It  is  quite  noticeable  that  a  large  number  of  the  investi- 
gators of  the  properties  of  nonaqueous  solutions  express  the 
thought  that  there  is  manifested  considerable  influence  be- 
tween the  dissolved  substance  and  the  solvent.  This  factor 
of  the  influence  of  the  solvent  upon  the  dissolved  substance 
is  one  that  is  no  doubt  of  very  great  importance  ;  and  in  the 
development  of  the  electrolytic  dissociation  theory  (which 
is  based  upon  the  behavior  of  aqueous  solutions)  the  action 
of  the  solvent  upon  the  dissolved  substance  has  been  entirely 
neglected. 


408  PHYSICAL  CHEMISTRY 

Fitzpatrick  concludes  from  his  investigation  on  the  conduc- 
tivity of  alcoholic  solutions  that  the  action  of  the  solvent  upon 
the  dissolved  substance  is  a  chemical  one.  He  conceives  the 
dissolved  salt  as  decomposing  and  forming  molecular  groups 
in  the  solvent.  Owing  to  the  large  excess  of  the  solvent  there 
will  be  a  continual  decomposition  and  recombination  of  these 
molecular  groups.  He  cautions  one  against  regarding  the 
solvent  as  a  medium  in  which  the  salt  particles  are  suspended 
or  as  a  dissociating  agent.  Wildermann,  on  the  other  hand, 
recognizes  two  kinds  of  dissociation  —  one  the  electrolytic 
dissociation  of  the  dissolved  substance,  and  the  other,  the 
dissociation  of  the  larger  molecular  aggregates  into  smaller 
ones.  For  example,  in  a  solution  of  KC1  in  water  the  follow- 
ing aggregates  are  assumed  to  exist :  K2C12,  KC1,  K2+C1, 
KC1~2,  K+,  and  Cl~.  He  further  maintains  that  solutions 
of  all  substances,  whatever  the  solvent  or  concentration, 
undergo  electrolytic  dissociation. 

Cattaneo  was  impressed  with  the  fact  that  the  molecular 
conductivity  is  greatly  influenced  by  the  nature  of  the  solvent 
employed.  He  was  not  able,  however,  to  point  out  any  direct 
relation  existing  between  the  various  properties  of  the  sol- 
vents .which  yield  solutions  that  conduct.  Konovaloff, 
from  his  work  on  the  amines,  concludes  that  only  those  sol- 
vents that  react  chemically  with  the  dissolved  substance 
yield  solutions  that  conduct.  It  is  true  that  there  are  many 
solvents  of  this  nature  which  do  react  with  the  dissolved  sub- 
stance, and  yet  which  do  not 'yield  solutions  that  conduct 
electricity.  Picric  acid  reacts  with  benzene,  but  the  result- 
ing solution  does  not  conduct  electricity.  Hence  chemical 
combination  of  the  dissolved  substance  with  the  solvent  may 
take  place  and  yet  the  solutions  need  not  necessarily  conduct. 
Werner  has  isolated  and  analyzed  a  large  number  of  products 
of  pyridine  and  piperidine,  among  those  of  other  organic  sol- 
vents, with  salts  of  the  heavy  metals.  From  the  boiling 
point  determinations,  the  molecular  weights  of  these  salts 


NONAQUEOUS  SOLUTIONS  409 

seem  to  be  very  slightly  influenced  by  their  union  with  the 
solvent.  This  is  analogous  to  the  fact  that  salts  which  crys- 
tallize from  an  aqueous  solution  with  water  of  crystallization 
yield  the  same  molecular  weights  whether  dissolved  in  the 
anhydrous  form  or  with  their  water  of  crystallization. 
Carrara  thinks  that  the  union  of  solvent  and  dissolved  sub- 
stance accounts  for  the  slight  conductivity  in  certain  cases. 
The  low  values  for  A  in  the  case  of  acetone  solutions  of  HC1 
and  LiCl  he  attributes  to  this  fact. 

It  has  been  pointed  out  by  Ciamician  that  the  dissociative 
power  of  a  solvent  depends  principally  upon  its  chemical 
structure.  That  is,  compounds  of  the  same  chemical  type, 
for  example,  of  the  HOH  type,  yield  solutions  that  conduct 
well.  This  is  true  in  the  case  of  alcoholic  solutions,  which 
are  not  the  only  class  of  compounds  that  possess  dissociative 
power,  as  has  already  been  pointed  out.  In  general,  how- 
ever, if  one  member  of  a  particular  type  of  compounds  (e.g. 
nitriles)  yields  solutions  that  conduct,  it  has  been  found  that 
other  members  also  possess  this  property ;  and  if  a  member 
of  some  other  type  (e.g.  hydrocarbons),  is  found  not  to  yield 
solutions  that  conduct,  other  members  do  not  possess  dis- 
sociative power. 

The  data  collected  are  as  yet  insufficient  to  show  what  the 
relation  between  solvent  and  dissolved  substance  must  be  in 
order  to  yield  solutions  that  conduct  electricity.  Enough 
facts  have  been  presented,  however,  to  make  it  apparent  that 
any  theory  that  aims  to  explain  the  electrical  conductivity 
of  solutions  in  general  must  take  into  consideration  the  in- 
fluence of  the  solvent  upon  the  dissolved  substance.  This 
subject  is  replete  with  interest ;  for  closely  connected  with  it 
is  the  true  cause  of  the  solubility  of  substances. 


CHAPTER   XXXIV 
THERMOCHEMISTRY 

IN  the  consideration  of  the  various  chemical  reactions  no 
account  is  usually  taken  of  the  energy  changes  accompanying 
them.  But  it  is  fully  recognized  now  that  the  thermal  change 
which  results  from  the  reaction  may  so  modify  the  tempera- 
ture of  the  system  that  the  best  results  are  not  obtainable  and 
consequently  it  is  necessary  to  control  the  temperature  very 
carefully,  as  it  is  only  over  a  small  range  of  temperature,  rela- 
tively, that  the  particular  reaction  takes  place  best.  In  a  few 
special  industrial  applications  only  is  the  energy  manifest  in 
the  thermal  changes  considered  of  sufficient  importance  to 
be  utilized.  In  the  combustion  of  fuel,  which  is  a  chemical 
reaction  consisting  of  the  union  of  oxygen  and  the  constituents 
of  the  fuel,  the  reaction  is  carried  on  for  the  sole  purpose  of 
obtaining  the  energy  in  the  form  of  heat.  The  study  of  the 
heat  energy  changes  associated  with  and  accompanying 
chemical  reactions  and  changes  constitute  what  is  termed 
Thermochemistry. 

A  large  amount  of  thermochemical  data  has  been  ob- 
tained, but  most  of  this  was  collected  some  time  ago  when  the 
field  of  chemical  reactions  was  confined  to  a  comparatively 
small  range  of  temperature  —  being  only  a  few  hundred 
degrees  above  ordinary  room  temperature.  By  the  use  of 
such  appliances  as  the  electric  furnace  the  temperature  range 
for  chemical  reactions  has  been  so  extended  that  entirely  new 
conditions  have  been  provided  which  have  resulted  in  the 
production  of  entirely  new  types  of  chemical  reactions.  The 

410 


THERMOCHEMISTRY  41 1 

thermal  energy  changes  accompanying  these  reactions  are 
entirely  different  from  those  of  the  analogous  reactions  under 
ordinary  conditions,  and  the  thermochemical  data  available 
for  these  are  not  applicable  to  the  new  conditions,  nor  are  the 
data  for  these  new  reactions  under  the  new  conditions  avail- 
able. Richards  1  states  that  the  available  thermochemical 
data  "  enable  us  to  figure  out  easily  the  energy  of  a  chemical 
reaction  beginning  and  ending  at  ordinary  temperatures, 
when  the  heats  of  formation  of  all  the  substances  concerned 
are  contained  in  the  tables.  They  give  us  no  exact  informa- 
tion at  all  about  the  energy  of  the  chemical  reaction  at  tem- 
peratures other  than  the  ordinary  room  temperature.  .  .  . 
A  larger  part  of  metallurgical  reactions  are  carried  on  at  tem- 
peratures above  the  ordinary,  running  up  to  3000°  C.  in 
electric  furnaces.  But,  for  any  temperature  above  the  ordi- 
nary, the  thermochemical  data  are  not  exact,  and  the  energy 
involved  in  the  reaction  is  different  from  what  it  is  beginning 
and  ending  at  room  temperature." 

Units  of  Thermochemistry.  —  The  amount  of  heat  is 
measured  in  a  number  of  different  units.  Those  employed 
in  technical  work  differ  from  those  used  in  scientific  investi- 
gations. The  unit  most  extensively  used  is  the  i5°-calorie. 
which  is  the  amount  of  heat  required  to  raise  one  gram  of 
water  i°  C.,  the  mean  temperature  being  15°  C.  On  page 
91  we  saw  that  the  specific  heat  of  water  is  different  at  dif- 
ferent temperatures,  and  so  the  value  of  the  calorie  varies 
with  the  temperature  taken. 

The  Bureau  of  Standards  employs  the  20°-calorie. 
Affirming  that,  "  In  view  of  the  greater  convenience  of  20° 
as  a  working  temperature,  smaller  rate  of  variation  in  the 
heat  capacity  of  water  at  this  temperature,  and  the  fact 
that  calorimetric  observations  are  commonly  made  at 
temperatures  near  this,  it  appears  desirable  to  follow  what 
seems  to  be  a  growing  tendency  among  experimenters  and 

1  J.  W.  Richards,  /.  /.  E.  C.,  9,  1056  (1916). 


f 

412  PHYSICAL   CHEMISTRY 

adopt  the  20°  as  the  basis  for  expressing  the  results  of  this 
investigation." 

"  Although  the  calorie  has  been  adopted  as  the  primary  unit 
of  heat,  the  extreme  precision  with  which  electrical  measure- 
ments can  be  made  has  led  to  the  use  of  the  joule  expressed 
in  electrical  units,  as  a  calorimetric  unit.  Such  use  involves 
the  acceptance  of  a  specific  value  for  the  ratio  /  of  the  joule 
to  the  calorie,  when  results  are  to  be  expressed  in  calories. 
The  adoption  of  such  secondary  units  is  hardly  justifiable 
unless  greater  comparative  accuracy  can  be  obtained  thereby. 
—  Investigation  seems  to  show  that  this  is  not  true ;  .  .  . 
therefore,  the  calorie  should  be  adopted  for  work  of  this  kind 
.  .  .  and  the  incidental  value  of  J  (one  20°  cal  =  4.181 
joules)  will  serve  as  an  excellent  check  on  the  other  measure- 
ments. .  .  ."  l 

The  following  heat  units  are  employed : 

The  Gram  Calorie  (cal.) 

The  15°  calorie  is  the  heat  required  to  raise  one  gram  of  water  i° 

at  the  mean  temperature  of  15°  C.  or  60°  F. 

The  20°  calorie  is  the  heat  required  to  raise  one  gram  of  water  one 

degree  at  the  mean  temperature  of  20°. 

The  mean  calorie  is  one  one-hundredth  of  the  heat  required  to  raise 

one  gram  of  water  from  o°  to  100°  C.     This  is  practically  the  same 

as  the  15°  calorie. 
The  Kilogram  Calorie    (Cal.)  is  1000  times  the  gram  calorie ;  i.e.  the 

heat  required  to  raise  one  kilogram  of  water  one  degree. 
The  Ostwald  Calorie  (K)  is  the  heat  required  to  raise  one  gram  of  water 

from  o°  to  1 00°  C.  and  is  also  termed  the  average  calorie.     This  is 

practically  100  times  the  value  of  the  15°  calorie. 
The  Pound  Calorie  (pound  cal.  or  Calb.)  is  the  heat  required  to  raise 

the  temperature  of  one  pound  of  water  i°  C. 
The  British    Thermal    Unit  (b.  t.  u.)   is  the  amount  of  heat   required 

to  raise  the  temperature  of  one  pound  of  water  i°  F.,  from  60  to  61°  F. 
The  Evaporation  Unit  is  the  amount  of  heat  required  to  convert  one 

pound  of  water  at  212°  F.  into  steam  at  the  same  temperature,  at 

normal  atmospheric  pressure. 

1  Bull.  Vol.  u,  220  (1915). 


THERMOCHEMISTRY  413 

The  relation  between  the  various  heat  units  may  be  ex- 
pressed as  follows : 

b.  t.  u.  =  252  cal. 

Evaporation  Unit  =  967  b.  t.  u. 

15°  cal.  =4.186  joules  (or  4.2) 

20°  cal.  =4.181  joules  (Beau.  Stan.) 

watt  hour  =  0.86  Cal. 

Specific  Heats.  —  The  specific  heat  capacity,  C,  is  defined 
as  the  amount  of  heat  required  to  raise  one  gram  of  the  sub- 
stance one  degree.  This  amount  will  of  course  depend  upon 
the  temperature  of  the  substance  as  well  as  upon  its  physical 
state,  for  the  capacity  for  heat  of  a  body  varies  with  these 
factors.  Hence  it  is  necessary  to  designate  both. 

The  atomic  heat  of  an  element  is  the  specific  heat  multiplied 
by  the  atomic  weight.  Dulong  and  Petit  stated  (1819) 
that  this  value  is  a  constant  quantity,  i.e.  the  capacity  of 
atoms  for  heat  is  practically  the  same  for  all  solid  elements. 
This  is  Dulong  and  Petit 's  Law.  The  value  of  the  constant 
varies  between  6  and  7  with  an  average  of  6.4.  It  was  chiefly 
upon  the  accurate  determinations  of  Regnault  of  the  specific 
heats  of  the  metals  at  ranges  of  temperatures  from  10  to  100° 
that  this  generalization  was  based  and  consequently  there 
were  many  marked  exceptions.  The  most  pronounced  ex- 
ceptions are  carbon,  silicon,  and  boron.  By  using  the  specific 
heats  of  these  elements  at  higher  temperatures,  the  atomic 
heat  approaches  more  nearly  that  of  the  constant  6.4. 

The  following  values  show  the  most  marked  variations : 

.  Element  Al          B          Be         C          Si          P          S 

Atomic  heat          5.4        2.8         3.7        1.8        4.5        5.9       5.7 

The  variation  from  the  constant  becomes  less  marked  if 
the  specific  heat  at  higher  temperatures  is  employed.  The 
values  given  in  Table  LXXIII  illustrate  the  change  of  the 
specific  heat  with  the  temperature. 


414 


PHYSICAL   CHEMISTRY 


TABLE  LXXIII 


ALUMINIUM 

BORON 

Temp. 

Sp.  Heat 

At.  Heat 

Temp. 

Sp.  Heat 

At.  Heat 

0° 

0.2089 

5.66 

26.6° 

0.2382 

2.62 

IOO 

0.2226 

6.04 

76.7 

0.2737 

3-01 

625 

0.3077 

8-34 

125.8 

0.3069 

3-37 

233-2 

0.3663 

4.04 

BERYLLIUM 

SILICON 

Temp. 

Sp.  Heat 

At.  Heat 

Temp. 

Sp.  Heat 

At.  Heat 

23° 

0.397 

3-61 

-135° 

0.0861 

2-44 

73 

0.448 

4.08 

+   24 

O.I7I2 

4-85 

157 

0.519 

4-73 

128.7 

0.1964 

5-56 

257 

0.582 

5-29 

232.4 

0.2029 

5-74 

GRAPHITE 

DIAMOND 

Temp. 

Sp.  Heat 

At.  Heat 

Temp. 

Sp.  Heat 

At.  Heat 

-     50.3 

0.1138 

1.36 

~  50.5 

0.0635 

0.762 

+     10.8 

0.1604 

1.92 

+  10.7 

O.II28 

1-35 

138.5 

0.2542 

3-05 

85-5 

0.1765 

2.12 

249-3 

0.3250 

3-90 

206.1 

0.2733 

3-28 

641.9 

0.4450 

5-34 

606.7 

0.4408 

5-29 

977.0 

0.4670 

5-60 

985.0 

0.4589 

5-51 

o°  -  3000° 

0-535 

6.42 

The  values  for  graphite  and  for  diamond  show  that  the 
specific  heats  of  allotropic  modifications  of  elements  are 
different  at  low  temperatures,  but  at  high  temperatures  this 
difference  becomes  less  marked. 

The  atomic  heat  constant,  6.4,  may  be  employed  as  a 
means  for  determining  the  atomic  weight  of  elements,  since 
the  atomic  weight  X  specific  heat  =  6.4.  Hence,  knowing 


THERMOCHEMISTRY 


415 


the  specific  heat  of  an  element,  its  atomic  weight  may  be 
calculated.  In  the  formulation  of  this  law  Dulong  and  Petit 
changed  the  accepted  value  of  the  atomic  weight  of  a  number 
of  the  elements.  For  example,  two  thirds  of  the  original 
value  for  bismuth  was  selected ;  twice  the  value  of  lead ; 
one  and  one  half  times  the  value  of  cobalt ;  and  one  half 
the  value  of  silver.  These  new  values  selected  were  all 
found  subsequently  to  be  the  true  ones. 

There  is  a  marked  difference  in  the  specific  heat  of  a  sub- 
stance, depending  upon  the  physical  state  in  which  it  exists. 
This  is  illustrated  in  the  case  of  water  by  the  following  data  : 


PHASE 

TEMPERATURE 

SPECIFIC  HEAT 

OBSERVER 

Ice 

—  78°  to  1  8° 

0.46^ 

Dewar 

Liquid             .... 

20° 

I.OOO 

Callender 

Vapor   

I  OO°  tO  2OO° 

0.465 

Holborn  and 

Henning 

Specific  Heat  of  Compounds.  —  Neumann  (1831)  showed 
that  the  specific  heat  multiplied  by  the  formula  weight  of  a 
compound  is  a  constant.  That  is,  the  molecular  heat  of  com- 
pounds similarly  constituted  is  nearly  equal.  Kopp  (1864) 
showed  that  as  the  molecular  weight  of  compounds  is  the 
sum  of  the  atomic  weights,  so  too  is  the  molecular  heat  the 
sum  of  the  atomic  heats.  This  is,  however,  not  universally 
true,  and  particularly  is  this  the  case  of  compounds  contain- 
ing the  halogens,  nitrogen,  and  oxygen.  In  homologous 
series,  Ostwald  has  shown  that  there  is  an  almost  constant 
difference  in  the  molecular  heats  of  the  compounds  corre- 
sponding to  the  specific  heat  of  the  group  CH2.  This  varies, 
however,  from  series  to  series.  Isomeric  compounds  should 
have  the  same  molecular  heat,  and  this  is  true  for  those  com- 
pounds that  are  similar  in  constitution,  but  those  that  differ, 
such  as  alcohols  and  aldehydes,  have  different  values. 


41 6  PHYSICAL  CHEMISTRY 

In  the  case  of  alloys,  the  specific  heat  is  almost  exactly 
the  sum  of  the  specific  heats  of  the  constituents,  and  this 
applies  to  mixtures  in  general,  as  well  as  to  compounds. 

The  specific  heat  of  water  varies  with  the  temperature, 
and  this  is  shown  by  the  values  given  in  Table  X.  For 
most  liquids  the  specific  heat  increases  with  an  increase  in  the 
temperature,  but  mercury  is  an  exception.  The  specific 
heat  of  twenty-seven  esters  of  the  aliphatic  series  can  be 
represented  by  a  linear  equation,  but  other  series  do  not 
give  as  good  an  agreement.  The  specific  heat  of  gases  has 
been  considered  in  Chapter  IX. 

Heats  of  Reactions.  —  The  heat  capacity  of  a  substance 
varies  with  its  state  of  aggregation ;  hence,  it  is  necessary  to 
designate  the  phase  in  which  the  material  under  discussion 
exists.  So,  in  writing  equations  representing  thermochemical 
reactions,  different  methods  are  employed  to  distinguish  the 
different  phases ;  the  following  is  the  usual  form  :  solid  [H^O], 
liquid,  H2O,  and  vapor  or  gas  (H2O).  In  ascertaining  the 
thermal  change  accompanying  a  chemical  reaction  it  is  not 
only  necessary  to  know  the  phase  in  which  the  reacting  sub- 
stances exist,  but  also  whether  there  is  a  change  from  one 
phase  to  another,  whether  the  substances  reacting  are  in  solu- 
tion, and  if  so  what  the  solvent  is,  and  also  the  concentration 
of  the  solution. 

The  H eat  of  Reaction  is  defined  as  the  number  of  calories 
of  heat  absorbed  or  evolved  by  the  reaction  of  stoichiometri- 
cal  quantities  of  the  substances  that  are  represented  by  the 
chemical  equation.  When  the  reaction  represents  the 
formation  of  a  substance,  it  is  termed  the  heat  of  formation; 
when  the  combustion  of  a  substance  is  represented,  it  is 
termed  the  heat  of  combustion  ;  when  the  process  of  neutrali- 
zation is  represented,  it  is  termed  the  heat  of  neutralization. 
Similarly  we  have  the  heat  of  solution,  heqt  of  dilution,  heat  of 
precipitation,  heat  of  ionization;  and  when  there  is  a  change  of 
state  involved,  we  have  heat  of  fusion  and  heat  of  vaporization. 


THERMOCHEMISTRY  417 

The  reaction  representing  the  formation  of  ferrous  oxide 
is  expressed  by  the  equation 

[Fe]  +  (O)  =  [FeO]  +  65,700  cal. 

which  shows  that  during  the  formation  of  one  mole  of  ferrous 
oxide  there  are  65,700  calories  of  heat  liberated.  In  the 
reaction  representing  the  decomposition  of  ferrous  oxide  there 
would  be  absorbed  this  same  quantity  of  heat  in  order 
to  obtain  the  original  conditions.  This  illustrates  what  is 
sometimes  called  the  First  Law  of  Thermochemistry,  which 
was  first  stated  by  Lavoisier  and  Laplace  in  1780.  This  may 
be  expressed  as  follows :  The  amount  of  heat  required  to  de- 
compose a  compound  into  its  elements  is  equal  to  the  heat  evolved 
when  the  elements  combine  to  form  the  compound. 

It  is  well  known  that  many  compounds  cannot  be  formed 
directly  from  the  elements,  and  so  the  heat  of  formation 
cannot  always  be  obtained  by  direct  means.  In  1840  Hess 
discovered  the  Law  of  Constant  Heat  Summation,  which  is 
the  fundamental  law  upon  which  all  thermochemical  calcu- 
lations are  based.  This  law  is  stated  as  follows :  The  total 
heat  effect  of  a  chemical  change  depends  only  on  the  initial  and 
final  stages  of  the  system  and  is  independent  of  the  intermediate 
stages  through  which  the  system  passes.  The  heat  of  the  reac- 
tion, then,  should  be  the  same  in  employing  different  methods, 
irrespective  of  the  number  of  different  processes  or  reactions 
involved  in  the  production  of  the  particular  substance.  This 
is  illustrated  in  the  formation  of  an  aqueous  solution  of  am- 
monium chloride. 

(NH8)  +  (HC1)  =  [NH4C1]  +  42,100  cal. 

[NH4C1]  +  aq  =  NH4Clqg  -     3,900  cal. 

Adding,    (NH3)  +  (HC1)  +  aq  =  NH4Clog  +  38,200  cal. 

Or,  (NH3)  +  aq  =  NH3ag      +    8,400  cal. 

(HC1)  +  aq  =  HClog       +  17,300  cal. 

Mixing,  NH3ag  +  HClag  =  NH4Cla<?  +  12,300  cal. 

Adding,    (NH8)  +  (HC1)  +  aq  =  NH4Clo^  +  38,000  cal. 


418  PHYSICAL   CHEMISTRY 

The  small  difference  in  the  heat  of  formation  of  an  aqueous 
solution  of  ammonium  chloride  by  the  two  methods  indicates 
that  it  is  immaterial  which  method  is  employed,  for  the  same 
heat  value  is  obtained. 

The  term  aq  signifies  that  such  a  quantity  of  water  has 
been  employed  that  upon  further  addition  of  water  the  heat 
of  dilution  is  practically  zero.  Hence  HClag  signifies  a 
dilute  aqueous  solution  of  HC1  such  that  the  further  addition 
or  subtraction  of  water  would  produce  no  appreciable  heat 
effect. 

Heat  of  Formation.  —  The  heat  of  formation  of  methane  is 
represented  by  the  following  equation, 

[C]  +  2  (H2)  =  (CH4)  +  22,250  cal. 
for  ethylene  by 

2  [C]  +  2  (H2)  =  (C2H4)  -  1 1, 2 50  cal. 

In  the  formation  of  methane  there  is  an  evolution  of  heat. 
Reactions  of  this  type  are  designated  exothermic,  and  the 
compound  is  termed  an  exothermic  compound.  There  is  a 
loss  of  heat  from  the  system  itself,  that  is,  an  evolution  of 
heat,  and  this  is  the  usual  type  of  thermochemical  reactions. 
In  the  formation  of  ethylene  there  is  an  absorption  of  heat  and 
the  reaction  is  termed  endothermic,  while  the  compound  is 
designated  an  endothermic  compound.  The  following  are 
endothermic  compounds:  Acetylene  absorbs  54,750  calories 
of  heat  in  the  formation  of  one  mole ;  [CaC2]  absorbs  6,259 
cal.;  (AsHa)  absorbs  44,200  cal.;  CS2  absorbs  25,400  cal. 
Endothermic  compounds  are  comparatively  unstable  and 
readily  decomposed,  sometimes  with  violence. 

Heats  of  Combustion.  —  Since  the  heats  of  combustion 
of  carbon  compounds  are  of  great  practical  importance  and 
the  values  are  comparatively  easily  determined,  the  values 
are  usually  employed  in  calculating  the  heats  of  formation 
of  compounds. 


THERMOCHEMISTRY  419 

Depending  upon  the  allotropic  modification  of  carbon 
employed,  different  values  are  obtained  for  the  heat  of 
formation  of  carbon  dioxide,  as  the  following  shows : 

[C]      diamond  +  (O2)  =  (CO2)  +  94,300  cal. 

[C]       graphite  +  (O2)  =  (CO2)  +  94,800  cal. 

[C]  amorphous  +  (O2)  =  (CO2)  +  97,200  cal.  (Richards) 

[C]  amorphous  +  (O)    =  (CO)   +  29,160  cal. 

The  heat  of  formation  of  carbon  monoxide  from  the  com- 
bustion of  carbon  cannot  be  determined  experimentally,  but 
it  can  be  obtained  indirectly  as  follows : 

[C]  amorphous  +  (O2)  =  (CO2)  +  97,200  cal. 
(CO)  +  (O)    =  (CO2)  +  68,040  cal. 

If  x  is  the  heat  of  formation  of  carbon  monoxide,  according 
to  Hess'  Law  x  -f-  68,040  =  97,200.  Solving,  we  have  %  = 
29,160,  or  subtracting  the  second  thermochemical  equation 
from  the  first,  we  have  C  —  (CO)  +  (O)  =  29,160  cal.,  or 

[C]  +  (O)  =  (CO)  -f  29,160  cal. 

Many  of  the  compounds  containing  carbon  are  of  particu- 
lar importance  as  fuels,  and  the  heat  obtained  by  burning 
them  is  utilized  as  a  source  of  heat  in  many  of  the  industries. 
Then,  too,  the  calorific  value  of  foods  which  are  oxidized  in 
the  body  in  order  to  maintain  its  normal  temperature  is 
assuming  more  and  more  importance  in  dietary  studies,  not 
only  for  the  human  race,  but  particularly  in  providing  bal- 
anced rations  for  animals. 

Calorific  Power  of  Fuels.  —  In  the  combustion  of  fuels 
water  is  one  of  the  products,  —  and  the  temperature  of  the 
furnace  is  such  that  the  water  is  usually  uncondensed.  So 
in  the  calculation  of  the  calorific  power  of  fuels,  in  order  to 
obtain  the  correct  heat  balance  sheet  for  the  furnace,  it  is 
necessary  to  consider  the  water  as  vapor,  for  the  condensa- 


420  PHYSICAL  CHEMISTRY 

tion  of  the  vapor  would  give  a  large  increase  in  heat  due  to 
the  latent  heat  of  condensation,  and  this  would  result  in  a  loss 
which  would  appear  in  the  waste  gases  and  thus  unduly  in- 
crease the  apparent  chimney  loss. 

In  the  calculation  of  the  calorific  power  of  fuels,  as  in  the 
combustion  of  other  substances,  Dulong  and  Petit 's  method 
is  employed.  That  is,  the  heat  value  is  obtained  by  assum- 
ing the  carbon  all  free  to  burn,  the  oxygen  present  combined 
with  hydrogen  in  the  ratio  2  Hz '.  O%,  and  the  excess  of  hydro- 
gen free  to  burn.  The  calorific  value  of  fuel  may  be  deter- 
mined directly  in  a  calorimeter  or  may  be  calculated  from  the 
analysis.  The  maximum  temperature  attainable  depends 
upon  many  factors,  among  which  are  the  conditions  under 
which  the  fuel  is  burned,  whether  the  fuel  is  cold  or  hot,  and 
whether  the  air  used  is  cold  or  has  been  preheated.  It  is 
not  possible  to  preheat  many  gaseous  fuels  because  they  are 
decomposed  and  carbon  is  deposited.  Another  important 
factor  is  the  heat  radiation  of  the  furnace,  which  introduces 
in  this  connection  the  construction  of  the  various  furnaces 
and  particularly  the  heat  conductance  of  materials ;  this  is 
becoming  one  of  the  important  departments  of  thermochem- 
istry. Particularly  is  this  true  of  electric  furnaces,  in  which 
the  external  source  of  heat  energy  is  supplied,  not  from  a 
fuel,  but  from  an  electrical  source,  and  also  sometimes  par- 
tially from  the  chemical  reactions  between  the  substances 
employed.  But  as  this  subject  requires  an  extended  discus- 
sion, reference  is  given  to  special  presentations,  such  as  The 
Electric  Furnace,  by  Stansfield,  Chapter  III. 

Methane  burns  according  to  the  following  thermochemical 
equation : 

(CH4)  +  (2  H2)  =  (C02)    +  (2  H20) 
22,250  +       o  97,200  +  2  X  58,060 

If  the  water  is  assumed  to  be  in  the  form  of  vapor,  its  heat  of 
formation  is  2  X  58,060  cal.,  and  the  heat  of  formation  of 


THERMOCHEMISTRY  42 1 

carbon  dioxide  from  amorphous  carbon  is  97,200  cal.,  which 
would  give  as  the  total  heat  liberated  in  the  formation  of  two 
formula  weights  of  water  and  one  formula  weight  of  carbon 
dioxide,  213,320  calories.  But  a  part  of  this  will  be  required 
to  decompose  the  methane,  and  this  quantity  will  be  equiva- 
lent to  the  heat  of  formation  of  methane,  which  has  been 
found  to  be  22,250  cal.  Then  the  difference,  191,070  cal.,  is 
the  heat  of  combustion  of  methane,  which  may  also  be  ob- 
tained by  adding  the  numerical  values  in  the  above  equation. 
In  the  case  of  the  combustion  of  ethylene  we  have  in  a 
similar  manner  the  following  equation : 

(C2H4)     +  (02)  =     2  (C02)     +    2  (H20) 
(—  11,250)  2  X  97,200  +  2  X  58,060 

In  the  formation  of  ethylene,  since  it  is  an  endothermic  com- 
pound, the  summation  of  these  heats  of  formation  would  be 

—  (—  11,250)  +  2  X  97,200  +  2  X  58,060  =  312,770  cal. 

as  the  heat  of  combustion  of  one  formula  weight  of  ethylene, 
assuming  that  both  the  products  of  combustion  are  gaseous. 
If,  however,  we  assume  the  water  vapor  to  condense,  then  its 
heat  of  formation  would  be  69,000  cal.  and  we  have 

—  (—  11,250)  +  2  X  97,200  +  2  X  69,000  =  343,650  cal. 

as  the  heat  of  combustion  of  ethylene  when  the  products 
are  gaseous  carbon  dioxide  and  liquid  water. 

For  endothermic  compounds  as  illustrated  by  ethylene, 
the  heat  of  combustion  is  greater  than  the  heat  obtainable 
if  the  amounts  of  carbon  and  hydrogen  in  the  compound 
were  burned  in  the  free  state ;  while  exothermic  compounds 
give  less  heat  than  could  be  obtained  by  the  direct  combus- 
tion of  free  carbon  and  hydrogen  equivalent  to  the  formula 
weight. 

The  heats  of  formation  as  well  as  the  heats  of  combustion 
of  a  few  of  the  more  common  compounds  are  given  in  Table 


422 


PHYSICAL   CHEMISTRY 


LXXIV.  The  products  of  the  reaction  are  assumed  to  be  gases 
and  the  water  formed  to  be  uncondensed.  Most  of  the  data 
are  from  Richard's  Metallurgical  Calculations. 

TABLE  LXXIV 


SUBSTANCE 

MOLECULAR  HEAT  IN  CALORIES 
(cal.) 

of  Formation 

of  Combustion 

Water 

H2O     .... 

58,060 

Methane 

CH4     .     .     .     . 

22,250 

191,070 

Ethane 

C2H6    .... 

26,650 

34!,930 

Ethylene 

C2H4    .... 

-  11,250 

321,770 

Benzene 

C6H6    .... 

-     7,950 

765,330 

Anthracene 

CuHio  .     .     .     . 

-  39,050 

1,690,000 

Acetylene 

C2H2    .... 

-  54,750 

307,210 

Hydrogen 

58,060 

Hydrogen  sulphide 

H2S      .... 

4,800 

122,520 

Carbon  bisulphide 

CS2       .     .     ,:    „ 

-  25,400 

Calcium  oxide 

CaO     .     .     .     / 

131,500 

Silica 

SiO2  

I8O,OOO 

Ferrous  oxide 

FeO     .     .     .     . 

65,700 

Ferric  oxide 

Fe2O3  .     .    v    . 

195,600 

Sulphur  dioxide 

SO2      .     . 

69,260 

Sulphur  trioxide 

S03      .     .     ,    . 

91,900 

That  the  ordinary  thermochemical  data,  or  zero  thermo- 
chemical  data  as  sometimes  called,  cannot  be  utilized  in 
the  study  of  chemical  equilibrium  at  high  temperatures  is 
illustrated  in  Preuner's  work  on  the  equilibrium  reaction  on 
the  reduction  of  Fe3O4  by  hydrogen.  He  obtained  the 
equilibrium  constant  of  the  following  reaction 

Fe304  +  4  (H2)  ^T  3  Fe  +  4  (H2O) 

at  different  temperatures,  and  showed  that  the  heat  value  of 
the  reduction  at  960°  is  —  11,900  cal.  Upon  the  basis  of 
the  ordinary  heats  of  formation  the  value  is  —  270,800  + 
4  X  58,060  =  —  38,560  cal.  From  which  Preuner  con- 


THERMOCHEMISTRY  423 

eluded  that  van't  Hoff's  formula  for  calculating  heats  of 
reaction  is  not  applicable  to  this  class  of  reactions.  But  J.  W. 
Richards  shows  from  the  following  calculations  that  this 
conclusion  is  not  justifiable. 

The  heat  in  the  products  at  960°  is 

3  Fe      =  3  X  56  X  (0.218  X  960  -  39)  28,560  cal. 

4  H2O  =  4(22.22  1.)  X  (0.34  X  960  +  .00015  X  960 2)       =  41,300 

69,860  cal. 
Heat  in  the  reacting  substances  at  960°  is 

Fe3O4  =  232  x  (0.1447  X  960  +  0.0001878  X  960 2)       =  72,384 
4  H2    =  4(22.22 1.)  X  (0.303  X  960  +  0.000027  X  960  2)    =  28,075 

100,459  cal. 

The  heat  of  reaction  at  960°  is  therefore  the  summation 
of  the  heats  of  the  reactions  beginning  and  ending  at  zero 
—  38,560  cal.  and  these  heats  of  the  compounds  at  960°, 
which  gives 

—  38,650  —  69,860  +  100,459  =  ~-  7j76i   calories,  which 

is  in  better  agreement  with  the  value  obtained  by  Preuner. 

The  following  example  illustrates  the  general  methods  em- 
ployed in  certain  types  of  thermochemical  calculations.  A 
natural  gas  was  found  by  analysis  to  have  the  following  per- 
centage composition  by  volume:  CH4,  94.16;  H2,  1.42; 
C2H4,  0.30;  00,0.55;  CO2,  0.27;  62,0.32;  N2,  2.80;  H2S, 
0.18.  The  following  solutions  are  desired :  What  would  be 
the  maximum  flame  temperature,  (i)  if  burned  cold  with  the 
theoretical  amount  of  cold  air  ;  (2)  if  burned  cold,  employ- 
ing air  preheated  to  iooo°? 

First  find  the  heat  of  combustion  of  one  cubic4  meter  of 
the  gas.  If  the  molecular  weights  of  the  constituents  are 
expressed  in  kilograms,  then  the  volume  will  be  22.4  cubic 
meters,  and  the  molecular  heat  of  combustion  the  values 
expressed  in  Table  LXXIV  in  kilogram  calories  (Cal.).  The 
heat  of  combustion  of  one  cubic  meter  will  be  this  value  di- 


424 


PHYSICAL   CHEMISTRY 


vided  by  22.4.  The  values  employed  are  for  22.22  as  used  by 
Richards  and  have  not  been  recalculated.  We  then  have  the 
following  for  the  heats  of  combustion : 

=         8,095.2  Cal. 
37-1  Cal. 
43.4  Cal. 
16.8  Cal. 
9.9  Cal. 
8,203.1  Cal. 

The  oxygen  needed  for  the  combustion  of  these  respective 
quantities  of  the  gases  can  be  readily  calculated  and  also 
the  air  necessary  to  supply  it.  These  values  are  given  in  the 
second  column  of  the  following  table : 

TABLE  LXXV 


CUBIC  METERS 

CH4 

0.9416 

X 

8,598 

H2 

0.0142 

X 

2,613 

C2H4 

0.0030 

X 

14,480 

CO 

0.0055 

X 

3,062 

H2S 

O.OOI8 

X 

5,513 

i  Cu. 
METER 
OF  GAS 
CONTAINS 

OXYGEN 
REQUIRED 
CUBIC 
METERS 

PRODUCTS  OF  COMBUSTION 

C02 

HzO 

S02 

N2 

CH4    .     . 

0.9416 

1.8832 

0.9416 

1.8832 





C2H4.     . 

0.0030 

O.OO9O 

O.OO6o 

O.006O 

— 

— 

H2      .     . 

0.0142 

O.O07I 

— 

0.0142 

— 

— 

CO     .     . 

0.0055 

0.00275 

0.0055 

— 

— 

— 

C02    .     . 

O.OO27 

— 

O.OO27 

— 

— 

— 

02       .     . 

0.0032 

0.0032 

— 

— 

— 

— 

N2      .     . 

O.O28O 

— 

— 

— 

— 

0.028 

H2S    .     . 

O.OOI8 

0.0027 

—  - 

O.OOI8 

0.0018 

— 

I.90I55 

0.9558 

1.9052 

0.0018 

0.0280 

Air  required  .     .     .9.14       also  furnished  "nitrogen                     7-238 

Total  N2  =                    7.266 

The  products  formed  will  contain  the  heat  generated  and 
at  the  temperature  t  attained  by  the  combustion  of  these 
gases.  These  products  will  contain  the  following  amounts 
of  heat : 


THERMOCHEMISTRY  42  5 

CUBIC  METERS  SP.  HEATS 

N2       =     7.266  X  (0.303  X  /  +  0.000027 12) 

H2O     =     1.9052  X  (0.34    X  t  +  0.00015    f) 

CO2      =      0.9558  X  (0.37     X  t  +  0.00027    I2) 

SO2      =     0.0018  X  (0.444  X  t  +  0.00027    ?) 

Total  heat    =    3.2044 1  +  0.00074057 12  =      8203  Cal.  as  deter- 
mined above. 

Solving,  we  find  t  =  1806°  the  temperature  of  the  flame 
attained  when  the  gas  and  air  employed  are  cold. 

Now  if  the  air  is  preheated  to  1000°,  we  have  i  m.3  of  air 
at  1000°  =  0.303  X  1000  +  0.000027  X  iooo2,  or  the  heat 
in  i  cubic  meter  of  air  at  1000°  =  3 30  Cal.,  and  in  9.14 
cubic  meters  of  air  at  1000°  =  3016  Cal.  Therefore, 
3.2044  /  +  0.00074057  t2  =  8203  +  3016  Cal.,  and  solving  we 
have  /  =  2288°  as  the  temperature  of  the  flame  providing 
air  preheated  to  1000°  is  employed. 

It  may  be  readily  shown  that  if  air  in  excess  of  the  theoreti- 
cal amount  required  to  burn  the  gas  be  employed,  the  heat 
obtained  by  the  combustion  would  be  required  to  raise  the 
temperature  of  this  mass  of  material,  and  as  a  result  the 
maximunl  temperature  of  the  flame  would  be  decreased  by 
an  amount  depending  upon  the  quantity  of  air  used  in  excess. 

Calorific  Value  of  Foods.  —  The  combustion  of  food,  which 
consists  of  a  mixed  diet,  is  not  exactly  the  same  in  the  body 
as  it  is  in  a  calorimeter.  About  98  per  cent  of  the  carbohy- 
drates and  95  per  cent  of  the  fats  are  digested  —  that  is, 
absorbed  by  the  body.  In  the  case  of  these  the  products 
of  combustion  in  the  body  are  the  same  as  in  the  calorimeter ; 
but  the  products  of  combustion  include  urea,  creatin,  uric 
acid,  etc.,  which  are  eliminated  in  this  form  from  the  body, 
hence  the  proteins  are  not  completely  burned  as  they  are 
in  the  calorimeter.  Therefore,  it  is  evident  that  the  physio- 
logical fuel  value  is  smaller  than  the  heat  of  combustion. 
This  is  apparent  from  the  values  of  the  heat  of  combustion 
and  the  physiological  fuel  values  of  a  few  foods  given  in 
Table  LXXVI. 


426 


PHYSICAL   CHEMISTRY 
TABLE  LXXVI 


FOOD 

HEAT  OF  COMBUS- 
TION PER  GRAM 

PHYSIOLOGICAL 
FUEL  VALUE 

Carbohydrates   ,/  . 
Cane  sugar 

1  OS  Cal 

4.0  Cal. 

Milk  sugar      
^'lalt  sugar                                    .     • 

374 

372 

Starch                  .     .               .     ..    »- 

4.  2O 

Fats                                                  *     . 

q.o  Cal. 

Butter                                 .     . 

0  2 

Olive  oil     

9-4S 

Proteins                         ....»; 

4.0  Cal. 

Albumin     .  
Casein   *    > 

5-8 
5-86 

The  summation  of  the  physiological  fuel  value  of  the 
amounts  of  these  three  food  types,  namely,  carbohydrates, 
fats,  and  proteins,  present  in  a  food  constitutes  what  is  termed 
the  physiological  fuel  value  of  the  food.  The  analysis  of 
foods  is  expressed  in  terms  of  the  three  types  of  foods  and 
moisture,  and  then  from  the  physiological  fuel  value  of  these 
the  fuel  value  of  the  food  is  calculated.  In  Table  LXXVII 
are  given  the  composition  of  a  few  typical  foods  and  the 
physiological  fuel  value  of  the  same : 

TABLE   LXXVII 


CHEMICAL  COMPOSITION 

FOOD  MATERIAL 

PARTS  PER  GRAM 

PHYSIOLOGICAL 

Protein 

Fat 

Carbohydrates 

Roast  beef  as  purchased 

0.236 

0.277 

0.300 

3.44  Cal. 

Bread,  white      .... 

0.093 

0.012 

0.527 

2.50  Cal. 

Eggs  as  purchased 

O.IIQ 

0.093 

— 

1.31  Cal. 

Milk,  whole       .... 

0.033 

0.040 

0.500 

0.69  Cal. 

Peanut  butter   .... 

0.293 

0.465 

O.I7I 

6.04  Cal. 

Peas,  canned      .... 

0.036 

0.002 

0.098 

0.55  Cal. 

Strawberry  as  purchased 

0.009 

0.006 

0.070 

0.37  Cal. 

THERMOCHEMISTRY 


427 


Heat  of  Solution.  —  When  a  solute  is  dissolved  in  water,  a 
change  in  temperature  is  usually  obtained.  If  the  quantity 
of  water  is  just  sufficient  to  produce  a  saturated  solution  of 
the  solute,  the  heat  change,  or  heat  tone  as  it  is  sometimes 
termed,  is  called  the  integral  heat  of  solution.  The  heat  of 
precipitation  is  of  the  opposite  sign  and  is  the  heat  absorbed 
or  evolved  when  the  solute  dissolves  in  a  nearly  saturated 
solution.  If  water  be  added  to  a  saturated  aqueous  solution, 
there  will  be  an  additional  heat  effect ;  then  if  more  solvent  be 
added,  the  change  becomes  less  with  the  successive  additions 
of  solvent  until  finally  no  further  thermal  change  is  noticed. 
So  if  one  mole  of  the  solute  be  added  to  an  indefinitely  large 
volume  of  solvent,  the  heat  effect  of  solution  is  the  maximum 
obtainable,  and  this  is  termed  the  heat  of  solution.  When  a 
solution  of  a  specified  concentration  is  diluted  to  an  infinitely 
large  volume,  the  heat  tone  of  this  reaction  represents  the 
difference  between  the  heat  of  solution  and  the  heat  tone 
of  the  original  solution,  and  this  difference  is  termed  the 
heat  oj 'dilution,  thatis,  the  heat  effect  obtained  by  diluting  the 
solution  to  that  of  a  solution  of  infinite  dilution. 


TABLE  LXXVIII 


HCl 

HNOS 

Moles  of  Water 

Heat  of  Solu- 
tion Cal. 

Heat  of  Dilu- 
tion Cal. 

Heat  of  Solu- 
tion Cal. 

Heat  of  Dilu- 
tion Cal. 

I 

5.38 



3-29 

— 

2 

11-37 

5-99 

— 

5 

14.96 

3-59 

6.67 

3-38 

10 

16.16 

1.20 

7-32 

0.65 

20 

16.76 

0.6O 

7.46 

0.14 

50 

17.12 

0.36 

— 

IOO 

17.24 

O.I2 

744 

—  O.O2 

300 

17.32 

0.08 

7-50 

O.04 

428 


PHYSICAL   CHEMISTRY 


The  heat  effects  obtained  by  diluting  a  solution  with  succes- 
sive quantities  of  water  are  also  designated  heats  of  dilution 
with  specified  quantities  of  water,  as  the  data  in  Table  LXXV 
show.  In  many  thermochemical  tables  the  heat  of  solution 
is  given  as  the  heat  tone  obtained  when  one  mole  of  the  sub- 
stance is  dissolved  in  the  specified  amount  of  solvent.  The 
heats  of  solution  given  are  the  values  for  the  quantity  of  water 
designated  in  each  case  and  the  heats  of  dilution  at  these 
dilutions  may  be  obtained  by  subtracting  the  value  at  any 
given  dilution  from  that  of  the  preceding  one  The  values 
given  under  heats  of  dilution  were  obtained  in  this  manner. 

Heat  of  Hydration.  —  The  combination  of  water  with 
many  substances  with  the  production  of  hydrates  is  accom- 
panied by  a  marked  thermal  change.  If  these  hydrates  are 
then  dissolved  in  water,  the  heat  of  solution  is  much  less  than 
when  the  anhydrous  salt  is  dissolved.  In  Table  LXXIX  the 
heat  of  hydration  of  a  few  common  hydrates  is  given.  The 
values  which  are  expressed  in  kilogram  calories  (Cal.)  repre- 
sent the  heat  tone  when  one  mole  of  the  solid  salt  combines 
with  the  quantity  of  liquid  water  specified,  forming  the  solid 
hydrate. 

TABLE   LXXIX 


SUBSTANCE 

WATER  OF 
HYDRATION 

HEAT  OF 
HYDRATION 

BaCl2    ........./    ':' 

H2O 

3.6  Cal. 

CuSO4  .     .     .     

2H2O 

5H2O 

7.0 

18.6 

KF 

2  H2O 

4.6 

K2CO3  

I.5H2O 

7.0 

Na2CO3                                             .     . 

H2O 

-14. 

Na2HPO4      ".•   .  «."-  .     .     .     .     *     . 

7H20 
ioH2O 
2  H2O 

I6.3 
21.8 

6.0 

C2H402      

7H20 
10  H2O 
2H20 

17-3 

28.5 

6.2 

THERMOCHEMISTRY  429 

Since  the  reaction  of  many  substances  takes  place  in  solu- 
tion, the  products  of  the  reaction  dissolve,  and  the  total 
heat  of  reaction  includes  the  heats  of  solution  and  is  then  ex- 
pressed as  the  heat  of  formation  in  dilute  solution. 

When  dilute  aqueous  solutions  of  salts  are  mixed,  there  is 
practically  no  heat  effect  providing  a  precipitate  is  not  formed. 
This  is  sometimes  referred  to  as  the  Law  of  Thermal  Neu- 
trality of  Salt  Solutions.  It  is  explained  upon  the  basis  of 
the  complete  ionization  of  the  salts  in  dilute  solutions,  which 
results  in  the  same  state  after  mixing  as  before,  and  conse- 
quently the  chemical  reaction  which  is  termed  double  decom- 
position (metathesis)  takes  place  with  no  concomitant  heat 
change.  While  in  the  case  of  such  exceptions  as  noticed  in 
mercury  and  cadmium  salts,  which  are  only  partially  disso- 
ciated, dilution  takes  place  by  mixing  the  solutions,  and  addi- 
tional dissociation  and  reaction,  accompanied  by  a  thermal 
effect  follow. 

When  precipitation  takes  place,  there  is  assumed  to  be  a 
change  in  the  ionic  concentration,  and  the  heat  effect  pro- 
duced is  that  of  precipitation.  The  molecular  heat  of  pre- 
cipitation should  be  the  same  by  whatever  means  the  precipi- 
tation is  accomplished  in  infinitely  dilute  solutions,  i.e.  for 
very  slightly  soluble  substances  such  as  silver  chloride. 

The  neutralization  of  an  acid  by  a  base  is  accompanied  by 
a  large  heat  effect,  and  upon  the  ionic  basis  the  equation 
representing  the  reaction  would  be 

H+C1-  +  Na+OH-  =  Na+Cl-  +  H20. 

This  indicates  that  the  only  change  is  the  disappearance  of 
the  hydrogen  and  hydroxyl  ions  with  the  formation  of  water 
which  remains  in  solution.  The  process  of  neutralization 
then  consists  of  the  formation  of  undissociated  water,  and  the 
heat  of  neutralization  should  be  the  same  per  mole  of  water 
formed,  irrespective  of  the  acids  or  bases  employed.  The 
data  in  Table  LXXX  illustrates  this  for  strong  acids  and  bases. 


f 

430  PHYSICAL  CHEMISTRY 

TABLE  LXXX  —  HEATS  OF  NEUTRALIZATION 


REACTION 

HEAT  OF 

NEUTRALI- 
ZATION 

REACTION 

HEAT  OF 
NEUTRALI- 
ZATION 

HClag  +  NaOHag    .     . 
HClag  +  KOHaq      .     . 
HClaq  +  i  Ba(OH)2ag  . 
HNO3ag  +  NaOHag  .    . 
HNO3aq  +  KOHaq  .    . 
HNO3aq  +  $  Ba(OH)2a? 
HBrag  +  NaOHag   .     . 

137  Cal. 
137 
13-9 
13-7 
13-8 
13.9 
13-7 

HClag  +  NH4OHag  .  . 
HFaq  +  KOHaq  .  .  . 
£  H2CO3ag  +  Na.OH.aq  . 
\  H2SO4ag  +  NaOHaq  . 
HNO3ag  +  NH4OHag  . 
HCNag  +  NaOHaq  .  . 
i  H2SO4ag  +  LiOHaq  . 

12.3 
I6.I 
10.  1 

15-7 

12.6 

2.9 
15.6 

When  the  reaction  involves  a  weak  or  moderately  strong 
acid  or  base,  there  is  not  the  uniformity  as  in  the  case  of 
strong  acids  and  bases,  as  is  shown  by  the  values  in  the  right- 
hand  part  of  the  above  table. 

By  replacing  the  hydrogen  of  polybasic  acids  successively, 
different  heat  effects  are  obtained.  In  this  case  there  is  the 
formation  of  acid  salts  as  intermediate  products.  The  data 
in  Table  LXXXI  illustrate  this  and  show  that  the  maxi- 
mum heat  effect  is  obtained  when  all  of  the  hydrogen  is 
replaced. 

TABLE  LXXXI 


MOLES  BASE 

H2S04atf 

H2CrO4atf 

HzCOsa? 

H3P040? 

I  NaOHag    .     . 

14-3  Cal. 

13.1  Cal. 

11.2  Cal. 

14.7  Cal. 

2  NaOHaq    .     . 

31-4 

24-7 

2O.2 

26.3 

3  NaOHag    .     . 

33.6 

4  NaOHaq    .     . 

31-4 

25-1 

2O.6 

I  KOHaq      .     . 

14.7 

13-4 

II.O 

2  KOHaq      .     . 

31-4 

25-4 

2O.2 

3  KOHag      .     . 

I  NH4OHag       . 

13-6 

22.2 

9-73 

13-5 

2  NH4OHag       . 

29.1 

22.2 

10.7 

26.3 

3  NH4OHag       . 

33-2 

THERMOCHEMISTRY  43 1 

Heat  of  lonization  or  Dissociation.  —  In  the  neutralization 
of  weak  acids  and  bases  the  heat  of  neutralization  is  quite 
different  from  the  normal  value  of  13.7  Cal.,  as  is  illustrated 
by  the  values  given  in  Table  LXXX.  In  the  process  of 
neutralization,  as  the  weak  component  is  not  completely  dis- 
sociated, there  must  be  a  gradual  dissociation  taking  place  in 
order  to  furnish  the  ions  of  water  which  combine  to  form  the 
undissociated  water.  Accompanying  this  process  of  gradual 
dissociation  there  is  the  concomitant  heat  change  due  to  the 
dissociation,  which  is  termed  the  heat  of  dissociation.  Ow- 
ing to  the  low  concentration  of  the  hydrogen  and  hydroxyl 
ions,  there  is  an  incompleteness  of  the  process  of  neutraliza- 
tion. Hence  this  variation  of  the  total  heat  effect  from 
the  value  13.7  Cal.  is  considered  as  the  heat  of  dissociation. 
That  is,  HD  =  HN  —  13.7,  in  which  HD  is  the  heat  of  dissocia- 
tion and  HN  is  the  heat  of  neutralization.  For  example,  in 
the  case  of  HCN,  where  a  is  practically  zero,  this  discrep- 
ancy amounts  to  2.9  Cal.  —  13.7  Cal.  or  —  10.8  Cal.,  while 
for  HF  we  have  16.1  —  13.7  =  +  2.7  Cal ,  which  values  are 
designated  the  heat  of  dissociation  of  HCN  and  HF  respec- 
tively. That  is,  the  quantity  of  heat,  13.7  Cal.,  is  involved 
in  the  process  of  neutralization  on  the  formation  of  one 
gram  mole  of  the  water  from  its  ions;  then  the  reverse 
operation  or  dissociation  of  water  into  its  ions  involves 
the  absorption  of  the  same  quantity  of  heat.  The  heat 
effect  is  —  13.7  Cal. 

The  heat  of  ionization  may  be  calculated  from  the  change 
of  the  dissociation  constants  obtained  from  Ostwald's  Dilu- 
tion Law  Equation  for  the  same  concentrations  at  two  differ- 
ent temperatures ;  or  direct  from  the  change  in  the  electri- 
cal conductance  with  the  change  in  the  temperature.  The 
heat  of  ionization  is  then  defined  as  the  heat  evolved  during 
the  dissociation  of  one  gram  mole  of  the  electrolyte.  The 
data  in  Table  LXXXII  give  an  idea  of  the  magnitude  of 
these  values  and  show  that  ionization  usually  takes  place 


432 


PHYSICAL  CHEMISTRY 


with  an  evolution  of  heat  and  refer  to  the  heat  evolved  in 
the  ionization  of  substances  already  in  solution. 

TABLE  LXXXII 


SUBSTANCE 

TEMPERATURE 

VOL.  IN  LITERS 

CAL. 

KCI  .  .  .  '.  \  .  .  . 

TS° 

IO 

4-  162 

NaCl 

•1C 

IO 

AC2 

LiCl   . 

•1C 

IO 

7QQ 

NaOH     
HC1    . 

35 

-1C 

10 
IO 

1292 
IO8O 

HNO3      .     ."  . 

•1C 

IO 

I  760 

HP     
Acetic  acid  
Salicylic  acid    . 

21-5 
10-50 

•IQ 

3.6 

10 
IOO 

3110 

-675 
—  6lQ 

Phenol     

"•5 

~  6025 

Ostwald  has  calculated  the  heat  of  ionization  of  metals 
from  the  thermochemical  data  obtained  by  the  replacement 
of  one  metal  by  another.  This  consists  of  the  transformation 
of  an  equivalent  quantity  of  a  metal  from  the  metallic  state 
into  the  ionic  condition.  The  heat  of  ionization  is  then 
practically  equal  to  the  heat  of  solution  of  one  gram-equiv- 
alent of  the  metal  in  a  very  dilute  solution  of  an  acid.  The 
data  in  Table  LXXXIII  are  some  of  Ostwald's  values. 

TABLE  LXXXIII 


ELEMENT 

HEAT  OF 
IONIZATION 
IN  CALORIES 

ELEMENT 

HEAT  or 
IONIZATION 
IN  CALORIES 

Aluminium  .... 
Lead  
Cadmium  .... 
Cuprous  Cu  .  .  . 
Cupric  Cu  .... 

+  40,700 
2OO 

+    9,20° 

-   15,800 

—    8  ooo 

Potassium     .     ... 
Magnesium        .     .    , 
Mercurous  Hg  .  ~  .     . 
Nickel       
Silver        .          ... 

+  61,800 

+  54400 
-  19,800 
+    8,000 

—  2^  ^OO 

Ferrous  Fe  .  .  .  . 
Ferric  Fe  .... 

+  II,  IOO 

-    3,ioo 

Hydrogen      .... 
Zinc      

O,O 
+  17,500 

CHAPTER  XXXV 
COLLOID    CHEMISTRY 

Diffusion.  —  We  are  familiar  with  the  fact  that  if  one 
gas  is  introduced  into  the  space  occupied  by  another,  the 
two  species  will  intermingle  and  they  will  soon  thoroughly 
mix.  The  mixture  will  be  uniform,  and  we  say  that  the  one 
gas  has  diffused  throughout  the  other.  If  a  bottle  of  per- 
fume is  opened  in  a  room,  the  odor  will  soon  be  distinguished 
in  all  parts  of  it.  The  perfume  has  diffused  throughout  the 
air  in  the  room.  Similarly,  if  sugar  is  placed  in  a  beaker  of 
water  and  allowed  to  stand,  the  sugar  will  subsequently  be 
found  in  all  parts  of  the  water.  The  same  is  true  of  other 
soluble  substances,  and  we  say  that  the  substance  dif- 
fuses throughout  the  water  and  will  eventually  occupy  all 
of  the  space  (volume  of  liquid)  allotted  to  it  as  the  gas  occu- 
pies the  volume  in  which  it  is  confined. 

We  have  seen  that  when  gases  are  brought  into  contact 
with  liquids,  the  amount  absorbe'd  depends  upon  the  particu- 
lar substances  selected  and  also  upon  the  temperature.  The 
absorption  is  also  accompanied  by  volume  changes  with  the 
concomitant  heat  change.  When  a  dry  rope  is  wet  with 
water,  there  is  a  marked  decrease  in  volume  accompanied  by 
an  evolution  of  heat.  This  fact  is  made  use  of  in  tightening 
the  ropes  of  a  sail.  The  water  saturates  the  soil  and  rocks 
in  a  similar  manner ;  we  say  that  oil  or  rock  absorbs  the 
water,  and  this  is  an  important  property,  making  the  supply 
available  for  plants.  How  does  the  water  travel  through 
the  rocks  and  soil  to  the  plants  ?  We  know  that  the  oil  passes 
up  through  the  wick  only  when  the  "  lamp  is  lighted,"  i.e. 
when  there  is  a  constant  removal  of  the  oil  from  the  end 

433 


* 

434  PHYSICAL  CHEMISTRY 

through  combustion.  The  oil  passes  through  the  fiber  of 
the  wick  by  a  process  termed  imbibition,  and  the  passage  of 
the  water  through  rocks  is  explained  by  the  same  process. 

We  have  previously  called  attention  to  the  passage  of  gases 
through  solids,  such  as  the  passage  of  hydrogen  through  the 
walls  of  platinum  tubes,  of  carbon  monoxide  through  red-hot 
iron  and  through  glass ;  and  also  of  the  diffusion  of  carbon 
into  iron,  and  copper  into  platinum,  as  examples  of  diffusion 
of  solids  into  solids. 

The  diffusion  of  solids  through  liquids  is  the  most  common 
and  has  been  extensively  studied.  If  CuSO4  is  placed  in  the 
bottom  of  a  tall  cylinder  filled  with  water,  the  liquid  becomes 
colored  but  very  slowly,  and  it  may  take  many  days  before 
the  solution  becomes  uniformly  colored.  If  a  few  crystals 
of  KMnO4  are  placed  on  the  bottom  of  another  cylinder 
filled  with  water,  the  liquid  is  colored  throughout  quickly, 
thus  showing  the  KMnQ4  diffuses  very  much  more  rapidly 
than  does  the  CuSO4.  That  is,  different  substances  have 
different  rates  of  diffusion. 

Work  of  Graham.  —  Thomas  Graham  (1861)  made  an 
extensive  study  of  the  diffusion  of  a  large  number  of  acids, 
salts,  bases,  and  organic  substances,  and  determined  their 
rates  of  diffusion.  He  found  that  the  rate  of  diffusion  is 
directly  proportional  to  the  concentration.  By  the  diffusion 
coefficient x  is  understood  in  this  case  the  number  of  grams 
of  the  substance  that  diffuses  upwards  per  day  when  the  con- 
centration at  each  horizontal  layer  differs  from  that  one 
centimeter  above  by  i  gram  per  cubic  centimeter. 

In  Table  LXXXIV  are  given  the  different  rates  of  diffusion 
in  water  of  a  few  substances. 

1  On  the  assumption  of  Frick's  Law  that  the  quantity  of  salt  which  diffuses 
through  a  given  area  is  proportional  to  the  difference  between  the  concentrations 
at  two  areas  infinitely  near  each  other,  the  diffusion  constant  or  specific  diffusion 
rate  is  "  equal  to  an  amount  of  the  solution  which  would  diffuse  across  the  unit 
area  under  a  concentration  gradient  of  unity  in  unit  time  if  the  rate  were  constant 
during  that  time  (days)." 


COLLOID   CHEMISTRY 
TABLE  LXXXIV 


435 


SUBSTANCE 

DAYS  FOR  DIFFU- 
SION OF  EQUAL 
QUANTITIES 

DIFFUSION  COEFFICIENT 
IN  ONE  DAY  (STEPHANE) 

Hydrochloric  acid   
Sodium  chloride 

I 
2  2"? 

1.  74  at      5° 
o  76  at     5° 

Cane  sugar          

7 

0.11  at     q° 

Magnesium  sulphate  .... 
Albumen 

7 

4.Q 

o  06  at    13° 

Caramel 

08 

0.05  at  10° 

That  is,  it  takes  98  times  as  long  for  caramel  to  diffuse  as  it 
does  for  the  same  quantity  of  hydrochloric  acid ;  or  7  times 
as  long  for  cane  sugar  as  for  the  same  quantity  of  hydrochloric 
acid.  The  diffusion  coefficient  of  cane  sugar  is  0.31  (9°), 
while  that  of  HC1  is  1.74  (5°),  and  of  caramel  0.05  (10°). 

Taking  the  amount  of  NaCl  which  diffuses  in  24  hours 
at  io°— 15°  through  parchment,  as  the  unit,  the  relative 
rates  for  a  few  other  substances  are  given  in  Table  LXXXV. 

TABLE  LXXXV 


SUBSTANCE 


RELATIVE  RATES  OF 
DIFFUSION 


NaCl  .  . 
Alcohol 
Glycerine  . 
Mannite  . 
Milk  sugar 
Cane  sugar 
Gum  arabic 


i.oo 

0.476 

0.440 

0-349 
0.185 
0.214 
0.004 


Graham  emphasized  from  his  data  that  these  substances 
could  be  divided  into  two  classes,  and  showed  that  of  those 
that  diffuse  fairly  rapidly  practically  all  manifest  the  prop- 
erty of  crystallization,  which  he  called  crystalloids;  while 
those  that  diffused  very  slowly,  which  he  called  colloids,  did 


436  PHYSICAL   CHEMISTRY 

not  possess  this  property,  but  gelatinized  on  separating  out, 
and  if  they  crystallized  at  all  it  was  only  after  a  very  long 
time. 

Dialysis.  —  Graham  showed  that  these  crystalloids  diffuse 
through  jellies  (gelatine,  agar,  etc.)  or  membranes  of  colloidal 
substances  approximately  as  rapidly  as  through  pure  water, 
while  by  these  the  colloids  are  completely  prevented  from 
diffusing.  This  led  Graham  not  only  to  emphasize  a  marked 
distinction  between  these  two  classes  of  substances,  but  also 
to  utilize  this  property  as  a  means  of  separation  of  crystal- 
loids from  colloids,  thus  giving  a  method  for  the  preparation 
of  solutions  of  colloids.  "  Of  all  the  properties  of  liquid  col- 
loids, their  slow  diffusion  in  water  and  their  arrest  by  colloidal 
septa  are  the  most  serviceable  in  distinguishing  them  from 
crystalloids." 

The  method  of  separation  by  diffusing  the  crystalloid 
through  a  septum  of  gelatinous  matter,  Graham  termed 
Dialysis,  while  to  the  whole  apparatus,  which  consisted  of  a 
glass  vessel  over  one  end  of  which  the  septum  is  drawn,  or 
the  septum  itself  in  the  form  of  a  tube,  he  gave  the  name 
Dialyzer.  One  of  the  best  and  most  extensively  used  dialytic 
septa  is  parchment  paper. 

One  illustration  of  this  method  for  the  preparation  of  col- 
loidal solutions  will  suffice.  Graham  says :  "  A  solution  of 
silica  is  obtained  by  pouring  sodium  silicate  into  dilute  HC1, 
the  acid  being  maintained  in  excess.  But  in  addition  to  HC1, 
such  a  solution  contains  NaCl,  a  salt  which  causes  the  silica 
to  gelatinize  when  the  solution  is  heated,  and  otherwise 
modifies  its  properties.  Now  such  soluble  silica,  placed  for 
twenty-four  hours  in  a  dialyzer  of  parchment  paper,  to  the 
usual  depth  of  10  mm.,  was  found  to  lose  in  that  time  5  per 
cent  of  its  silicic  acid  and  86  per  cent  of  its  hydrochloric  acid. 
After  four  days  on  the  dialyzer,  the  liquid  ceased  to  be  dis- 
turbed by  AgNO3.  All  of  the  chlorine  was  gone,  with  no 
further  loss  of  silica." 


COLLOID   CHEMISTRY  437 

The  preparation  of  colloid  solutions  of  metals  by  Bredig's 
sparking  electrode  method  consists  of  bringing  the  ends  of 
the  metal  electrodes  together  under  the  surface  of  the  liquid 
and  then  separating  them  so  as  to  form  an  arc.  By  repeat- 
edly touching  the  electrodes  together  and  separating  them  a 
colloid  solution  of  the  metal  may  be  formed.  Colloid  solu- 
tions may  also  be  obtained  by  employing  reducing  agents 
according  to  the  method  used  by  Carey  Lea. 

General  Character  of  Colloids.  —  In  our  consideration 
thus  far  we  have  denned  a  pure  chemical  compound  as  a 
substance  that  is  chemically  homogeneous.  The  method 
of  ascertaining  this  is  by  process  of  analysis,  and  in  the  case 
of  many  very  complex  substances  it  is  not  a  simple  matter 
to  determine  whether  the  constituents  present  conform  to 
the  Law  of  Definite  Proportions.  We  saw  in  the  considera- 
tion of  simple  binary  systems  that  by  variation  of  the  com- 
ponents we  could  obtain  fusion  curves  and  solubility  curves 
which  would  manifest  characteristic  properties  at  certain 
points,  from  which  we  conclude  the  existence  of  a  definite 
chemical  compound,  the  evidence  being  the  change  of  state 
without  change  in  temperature,  i.e.  a  constant  fusion  point, 
or  a  constant  freezing  point.  As  the  methods  have  become 
more  refined  the  increased  accuracy  of  the  measurements  has 
revealed  additional  chemical  compounds  (hydrates  in  many 
cases) .  So  by  the  use  of  new  methods  we  are  able  to  collect 
additional  information  concerning  the  relationship  existing 
between  the  components. 

In  the  discussion  of  binary  systems  we  met  a  type  of  solu- 
tions designated  solid  solutions.  These  conform  to  our  usual 
definition  of  solutions,  which  is,  a  phase  in  which  the  relative 
quantities  of  the  components  can  vary  continuously  within 
certain  limits,  or  a  phase  of  continuously  varying  concentra- 
tions ;  while  by  phase  we  understand  a  mass  that  is  chemi- 
cally and  physically  homogeneous.  So  it  is  evident  that  the 
identification  of  any  particular  phase  depends  upon  our 


438  PHYSICAL   CHEMISTRY 

ability  to  determine  whether  it  is  physically  homogeneous 
and  also  chemically  homogeneous,  and  this,  of  course,  is  de- 
pendent upon  the  degree  of  refinement  of  our  methods. 

Roozeboom  defines  a  homogeneous  system  as  one  in  which 
all  of  its  mechanically  separable  parts  show  the  same  chemi- 
cal constitution  and  the  same  chemical  or  physical  properties. 
"  Gases  and  liquids  which  have  been  well  mixed  possess  this 
homogeneity  of  constitution  because  of  the  smallness  of 
molecules  and  the  grossness  of  our  means  of  observation." 

The  attempts  to  determine  whether  a  system  is  a  solution 
have  led  to  such  definitions  of  a  solution  as  "  a  homogeneous 
mingling  "  ;  as  "  physical  mixtures  the  complexes  of  different 
substances  in  every  part  physically  and  chemically  homo- 
geneous," or,  as  Ostwald  states  it,  "  a  homogeneous  phase." 
The  basis  of  the  conception  of  solution,  then,  depends  not 
upon  the  many  properties  of  solutions  that  we  have  been 
discussing,  but  upon  the  question  of  the  homogeneity  or 
heterogeneity  of  the  system,  and  consequently  upon  our 
conception  of  and  our  means  of  determining  homogeneity. 

From  the  process  of  diffusion  we  have  seen  how  the  solute 
becomes  divided  and  subdivided  and  thus  distributed 
throughout  the  whole  of  the  solution.  Here  it  exists  in  such 
a  fine  state  of  division  that  we  are  unable  to  distinguish  any 
of  the  individual  particles  and  the  mass  (solution)  is  said  to 
be  homogeneous.  If  we  take  a  solution  of  colloidal  A1(OH)3, 
it  appears  perfectly  clear,  and  from  a  casual  observation  looks 
like  a  clear  solution  of  any  crystalloid  yielding  a  colorless 
solution.  The  same  is  true  of  many  other  colloid  solutions, 
a  microscopic  examination  of  which  would  not  reveal  the 
presence  of  any  of  the  diffused  substance  in  the  solution. 
If,  however,  a  convergent  ray  of  light  were  permitted  to  pass 
through  these  solutions,  it  would  be  possible  to  follow  the  ray 
through  the  solution  in  a  manner  similar  to  that  when  a 
bright  ray  of  light  passes  into  a  darkened  room  through  a 
small  orifice  in  the  curtain.  The  boundary  surfaces  of  the 


COLLOID   CHEMISTRY  439 

particles  of  dust  in  the  air  reflect  the  light,  and  they  are  thus 
made  visible  to  the  naked  eye ;  but  if  the  strong  ray  of  light 
passing  through  the  solution  is  examined  by  a  powerful 
microscope,  very  small  particles  can  be  readily  recognized. 
These  are  termed  ultramicroscopic  particles,  and  an  arrange- 
ment such  as  this,  making  use  of  the  strong  ray  of  light  (the 
Tyndall  effect)  and  the  microscope,  was  designed  by  Sie- 
dentopf  and  Zsigmondy  and  is  known  as  the  Ultramicro- 
scope.  By  use  of  this  method  a  solution  of  sodium  chloride 
would  appear  optically  homogeneous,  whereas  in  colloid 
solutions  there  would  be  a  lack  of  homogeneity.  It  is  con- 
ceivable that  the  particles  may  be  of  such  a  size  that  they 
would  be  recognizable  without  the  aid  of  the  microscope  and 
the  Tyndall  method  would  render  them  visible.  We  might 
imagine  the  particles  to  be  still  larger  and  of  such  size  that 
they  would  remain  suspended  in  the  liquid  only  a  relatively 
short  period.  In  this  latter  case  of  mere  suspension,  as  it  is 
termed,  we  would  have  a  case  readily  designated  as  hetero- 
geneous, for  the  boundaries  of  the  components  of  the  system 
could  be  readily  recognized.  It  is  therefore  conceivable 
that  we  may  have  all  degrees  of  division  of  matter  and  thus 
produce  a  continuous  gradation  of  sizes  of  particles,  from  the 
one  extreme  of  suspended  particles  through  those  of  micro- 
scopic and  ultramicroscopic  size  to  the  still  finer  ones,  which 
we  have  at  present  no  means  of  recognizing,  on  down  to  the 
ultimate  molecular  particles. 

Zsigmondy  says  :  "  We  see  that,  just  as  other  investigators 
have  said,  when  solutions  are  spoken  of  as  homogeneous  dis- 
tributions, mixtures,  etc.,  it  cannot  be  meant  that  they  are 
absolutely  homogeneous  mixtures.  If  such  great  homo- 
geneity is  demanded  of  solutions  that  we  can  detect  no  in- 
homogeneity  in  them  by  our  most  sensitive  methods,  we 
would  thereby  exclude  altogether  from  this  classification  solu- 
tions not  only  of  many  colloids,  but  also  of  numerous  crys- 
talloids, for  example,  fuchsin,  ferric  chloride,  chromic  chloride, 


440  PHYSICAL   CHEMISTRY 

saccharose,  raffinose,  and  solutions  in  the  critical  state.  We 
would  thus  run  a  risk  of  reducing  the  sphere  of  solutions 
every  time  we  increase  the  sensitiveness  of  our  methods  of 
investigation.  The  danger  can  be  easily  avoided  if  we  use 
the  word  '  solution '  in  its  usual  chemical  acceptance, 
meaning  thereby  subdivisions  which  appear  clear  in  ordinary 
daylight  and  which  cannot  be  separated  into  their  constitu- 
ents by  the  ordinary  mechanical  means  of  separation  (nitra- 
tion and  decantation)."  Wo.  Ostwald  emphasizes,  "  that 
it  is  not  the  presence  of  many  more  or  less  evident  particles 
which  may  be  recognized  either  macroscopically  or  microscop- 
ically that  distinguishes  a  colloid  from  a  true  solution.  It  is 
rather  the  intensity  of  the  unbroken  light  cone  passing  through 
the  solution  which  betrays  the  state  of  the  liquid.  It  is 
safe  to  say  that  liquids  which  show  no  definite  Tyndall  light 
cone  or  show  it  only  in  high  concentrations  are  true  (molecular- 
disperse)  solutions.  Practically  all  colloid  solutions  give  a 
positive  Tyndall  effect." 

It  is  generally  accepted  at  the  present  time  that  colloid 
solutions  are  regarded  as  heterogeneous  two-phase  systems, 
and  that  their  particular  distinguishing  properties  are  due 
principally  to  their  very  great  specific  surface,  and  thus  it  is 
evident  that  what  we  are  considering  is  really  a  state  of  matter 
and  should  refer  to  this  condition  as  the  colloid  state.  This 
was  fully  recognized  by  Graham,  for  he  states :  "  The  col- 
loidal is,  in  fact,  a  dynamical  state  of  matter  ;  the  crystalloidal 
being  the  statical  condition.  The  colloid  possesses  Energies. 
It  may  be  looked  upon  as  the  probable  primary  source  of  the 
force  appearing  in  the  phenomena  of  vitality.  To  the  grad- 
ual manner  in  which  colloidal  changes  take  place  (for  they 
always  demand  time  as  an  element),  may  the  characteristic 
protraction  of  chemico-organic  changes  also  be  referred." 

Classification  of  Colloid  Systems.  —  Various  methods  of 
classification  of  colloid  systems  have  been  used,  but  the 
classification  of  Zsigmondy  is  now  generally  employed.  This 


COLLOID   CHEMISTRY 


441 


is  based  upon  the  progressive  subdivision  of  the  given  phase. 
Considering  the  system  to  consist  of  two  phases,  we  have  one 
phase  being  distributed  throughout  the  other  phase.  The 
solvent  or  continuous  phase  is  termed  the  disperse  means, 
while  the  solute  is  termed  the  disperse  phase,  and  the  entire 
system  is  termed  a  dispersed  system  or  a  dispersoid  (which 
is  synonymous  with  colloid). 

As  the  subdivision  of  the  disperse  phrase  increases,  the  sur- 
face of  the  mass  increases  enormously.  This  is  illustrated 
in  Table  LXXXVI  given  by  Wo.  Ostwald. 

TABLE  LXXXVI  —  INCREASE  IN  THE  SURFACE  OF  A  CUBE 
WITH  PROGRESSIVE  DECIMAL  SUBDIVISION 


LENGTH  OF 

ONE  EDGE 

NUMBER 
OF  CUBES 

TOTAL  SURFACE 

SPECIFIC 
SURFACE 

I 

cm. 

I 

6 

square  cm. 

6 

I 

mm.  = 

X  10 

~x  cm. 

IO3 

60 

square  cm. 

6-  io1 

O.I 

mm.  = 

X  10 

~2  cm. 

IO6 

600 

square  cm. 

6-  io2 

O.OI 

mm.  = 

X  10 

-3  cm. 

IO9 

6000 

square  cm. 

6-  io3 

I.OO 

M        = 

X  10 

~4  cm. 

IO12 

6 

square  m. 

6-  io4 

(micron) 

O.I 

M        =• 

X  10 

~  5  cm. 

IO15 

60 

square  m. 

6-  io5 

O.OI 

/*        = 

X  10 

~  6  cm. 

IO18 

600 

square  m. 

6-  io6 

I.OO 

fJLfi          — 

X  10 

~  7  cm. 

lO2* 

6000 

square  m. 

6-io7 

O.IO 

w*      = 

X  10 

~  8  cm. 

IO24 

6 

hectares 

6-  io8 

O.OI 

fji/j.      = 

X  io 

~  9  cm. 

IO27 

60 

hectares 

6-  io9 

O.OOI 

W      = 

X  io 

~  10  cm. 

I030 

6 

square  km. 

6  •  io10 

The  specific  surface,  which  may  be  defined  as 

the  absolute  surface  of  the  entire  disperse  phase 
the  total  volume  of  the  disperse  phase 

is  one  of  the  marked  characteristics  of  a  system.  As  the 
specific  surface  increases,  the  subdivisions  become  smaller 
and  smaller,  and  we  say  that  the  dispersion  becomes  greater 
and  greater.  That  is,  the  degree  of  dispersion  increases,  and 


442 


PHYSICAL   CHEMISTRY 


instead  of  using  the  concept,  specific  surface,  this  other  ex- 
pression is  frequently  employed.  The  degree  of  dispersion 
is  also  used  synonymously  with  the  expression  colloidality. 

Hence  we  can  use  the  degree  of  dispersion  as  our  means 
of  classification  of  dispersoids,  and  since  there  is  a  gradual 
successive  subdivision,  the  colloidality  will  become  gradually 
more  pronounced  as  the  subdivision  of  the  particles  increases. 
As  there  are  no  marked  breaks  or  lines  of  demarcation,  our 
classification  must  be  made  arbitrarily,  and  the  basis  of 
this  is  the  relative  sizes  of  the  particles  and  our  means  of  dis- 
tinguishing them.  There  is,  however,  a  gradual  transition 
of  one  class  into  the  other. 

The  following  diagrammatic  representation  according  to 
Wo.  Ostwald  illustrates  the  classification  of  dispersoids : 


Molecular  and  super- 
molecular  dispersoids 
(Von  Weimarn's  solutoids) 

Size  of  particles  of  the  disperse  phase 
about  i  w  or  less 

Specific  surface  >  6  •  io7 


Colloid  Solutions 

Size   of   the   particles   of    the   dis- 
DISPERSOIDS  {   {  perse  phase  between  o.  i  A*  and  i  MA* 

Specific  surface  between  6-  io5  and 


True  or  coarse  dispersions 

(suspensions,  emulsions) 
Size  of  the  particles  of  the  disperse 

phase  greater  than  o.i  /* 
Specific  surface  <  6  •  io5 


The  particles  larger  than  about  o.i  /x  in  diameter  — 
which  represents  the  limit  of  microscopic  visibility  and  which 
is  taken  as  the  lower  limit  of  dispersion  —  constitute  the 
Suspensions  and  Emulsions.  Colloid  solutions  comprise  the 
particles  between  o.i  //.  and  i  /x/x  in  size.  By  the  ultra- 


COLLOID  CHEMISTRY  443 

microscope  particles  smaller  than  about  6  /A/A  have  not  been 
recognized,  and  the  lower  limit  has,  therefore,  been  placed  a 
little  beyond  the  range  of  vision  of  our  present  instruments. 
Their  degree  of  dispersion  is  between  6  •  io5  and  6  •  io7.  Dis- 
persoids  with  a  degree  of  dispersion  greater  than  6  •  io7  are 
known  as  molecular  dispersoids,  which  comprise  Graham's 
Crystalloids.  The  following  illustrate  the  sizes  of  some  of 
the  molecular  species:  Hydrogen  gas,  0.067  to  0.159  /A/A; 
water  vapor,  0.113  /A/A;  carbon  dioxide,  0.285  /A/A;  sodium 
chloride,  0.26  /A/A;  sugar,  0.7  /A/A. 

Additional  Nomenclature.  —  Owing  to  different  methods 
of  classification  of  dispersoids  a  large  number  of  terms  appear 
in  the  literature,  and  it  is  necessary  to  become  familiar  with 
them.  Depending  upon  which  phases  are  taken  for  the  dis- 
perse means  and  for  the  disperse  phase,  we  have  as  in  true 
solutions  nine  different  combinations  and  possible  "  solutions." 

I.    Liquid  as  the  disperse  means  ;  when  the  disperse  phase  is  a 

(a)  Solid,  they  are  termed  suspensions. 

(b)  Liquid,  they  are  termed  emulsions. 

(c)  Gas,  they  are  termed  foams. 

II.   Gas  as  the  disperse  means ;   we  have  when  the  disperse  phase  is 

(a)  Solid  —  smoke  (tobacco  smoke) ;  condensing  vapors  of  metals 

(ammonium  chloride,  etc.) ;    cosmic  dust,  etc. 

(b)  Liquid  —  atmospheric  fog,  clouds,  condensations  of  steam,  etc. 

(c)  Gas  —  no  example  known. 

III.    Solid  as  the  disperse  means ;  we  have  when  the  disperse  phase  is 

(a)  Solid  —  known   as    solid   solutions,    mixed    crystals,    carbon 

particles  in  iron,  etc. 

(b)  Liquid  —  occlusion  of  water,  inclusion. 

(c)  Gas  —  solutions    of    gases    in    solids,    gaseous    inclusions    in 

minerals. 

This  classification  is  then  in  harmony  with  Bancroft's 
definition :  "  Colloid  chemistry  is  the  chemistry  of  bubbles, 
drops,  grains,  films,  and  filaments." 

Graham  gave  the  name  sols  to  those  dispersoids  which  we 
usually  designate  colloids,  the  degree  of  dispersion  of  which 


444  PHYSICAL  CHEMISTRY 

lies  between  6  •  io5  and  6  •  io7.  If  the  degree  of  dispersion  de- 
creases below  the  lower  limit  of  colloids,  then  the  system  be- 
comes microscopically  heterogeneous  and  the  dispersoid  is 
said  to  exist  in  the  gel  condition.  There  is,  therefore,  a  loss 
of  uniform  distribution  of  the  disperse  phase  throughout  the 
disperse  means.  In  the  case  of  colloid  silicic  acid  Graham 
called  this  solution  a  sol;  after  the  silicic  acid  precipitated 
into  a  jelly-like  mass  he  applied  the  term  gel  to  the  precipitate. 
Various  terms  are  employed  to  express  this  change,  which  re- 
sults in  a  decrease  in  the  degree  of  dispersion,  and  the  disperse 
phase  is  said  to  coagulate,  precipitate,  gelatinize,  clot,  set,  etc. 
The  reverse  of  this  process  was  designated  by  Graham  pep- 
tization,  and  represents  the  dispersion  of  the  disperse  phase 
throughout  the  disperse  means.  If  for  any  dispersoid  the 
degree  of  dispersion  can  be  increased  and  also  decreased  at 
will,  so  as  to  change  the  state  by  reversing  the  conditions 
which  brought  about  the  change,  it  is  said  to  be  reversible. 
If  this  cannot  be  done,  it  is  irreversible. 

Depending  upon  the  character  of  the  disperse  means  we 
may  have,  when  water  is  the  disperse  means,  hydro  sols  and 
hydro  gels ;  with  alcohol,  ale  o  sols  and  ale  o  gels.  In  general, 
when  the  disperse  means  is  an  organic  liquid  the  dispersoid 
is  termed  an  organosol  or  an  organogel.  And  to  designate 
the  substance  in  the  disperse  phase  a  prefix  is  employed,  i.e., 
if  gold  is  the  disperse  phase  and  water  the  disperse  means, 
then  we  have  gold-hydrosol,  etc. 

The  Colloid  State.  —  Hundreds  of  substances  have  been 
obtained  as  colloids,  and  these  comprise  elements  as  well  as 
practically  all  types  of  chemical  compounds  ;  and  it  has  been 
recently  emphasized  that  the  possibility  of  converting  a  sub- 
stance into  the  colloidal  state  has  no  relation  whatever  to  the 
chemical  character  of  the  substance.  The  conception  that 
the  colloid  solutions  are  a  special  class  of  disperse  systems 
leads  to  the  acceptance  of  the  universality  of  the  colloid 
state.  Just  as  we  say  that  all  substances  are  soluble,  so  with 


COLLOID   CHEMISTRY  445 

the  proper  conditions  all  substances  can  be  sufficiently  dis- 
persed in  the  proper  disperse  means  to  have  a  degree  of  dis- 
persion sufficient  to  produce  particles  of  the  size  we  define  as 
belonging  to  the  division  designated  colloid  solutions.  As 
there  are  different  degrees  of  solubility,  so  there  is  a  marked 
difference  in  the  ease  with  which  various  substances  assume 
the  colloid  state,  for  it  is  a  state  or  condition  of  matter.  The 
study  of  the  colloid  state  comprises  colloid-chemistry,  which  is 
an  important  division  of  physical  chemistry  and  is  assuming 
as  prominent  a  place  as  electrochemistry,  thermochemistry, 
actino-chemistry,  and  radio-chemistry.  Wo.  Ostwald  states 
that,  "  Colloid-chemistry  deals  with  the  relations  of  the  sur- 
face energies  to  other  kinds  of  energy  as  shown  in  an  especially 
characteristic  way  in  dispersed  heterogeneous  systems." 

A  number  of  substances  are  known  to  exist  both  as  a  col- 
loid and  as  a  crystalloid.  Sodium  chloride,  which  is  usually 
known  as  a  crystalloid,  can  be  obtained  in  the  colloid  form, 
while  albumen,  which  is  usually  classed  as  a  colloid,  may  be 
crystallized 

It  is  conceivable  that  the  disperse  means  and  the  disperse 
phase  could  have  the  same  chemical  composition.  In  the 
case  of  a  number  of  liquids  the  Tyndall  effect  is  very  marked, 
which  shows  the  existence  of  a  heterogeneous  system,  i.e. 
there  is  a  disperse  phase  present.  This  has  been  noticed 
in  the  case  of  oils,  waxes,  different  varieties  of  rubber,  molten 
salts,  phosphoric  acid,  arsenious  acids,  etc.  These  are 
designated  isocolloids ;  and  if  the  substance  appears  in  allo- 
tropic  modifications,  the  colloid  system  is  termed  an  allo- 
colloid.  Sulphur,  phosphorus,  and  selenium  are  allocolloids. 
Posnjak  states  that  styrol,  C8H8,  polymerizes  into  (C8H8)n 
and  becomes  a  jelly-like  mass  or  glass-like  (metastyrol) , 
depending  upon  the  degree  of  polymerization.  "  If  one 
adds  to  pulverized  metastyrol  an  equal  weight  of  styrol, 
the  former  gradually  absorbs  the  latter.  In  the  process 
the  originally  opaque  powder  becomes  translucent  and 


446  PHYSICAL   CHEMISTRY 

gradually  changes  into  a  homogeneous,  gelatinous  or  jelly- 
like,  viscid,  transparent  mass.  If  less  styrol  is  added  to 
the  metastyrol,  —  say  only  about  a  fourth  as  much  of  the 
former  as  of  the  latter,  —  a  transparent  mass  results,  which 
is  not  viscid,  but  glossy." 

Two  allotropic  liquid  modifications  of  sulphur,  S\  and 
8,1,  are  recognized,  and  the  system  is  designated  an 
allocolloid,  for  over  a  certain  range  of  temperature  it  is  as- 
sumed that  the  dispersion  of  one  form  throughout  the  other 
conforms  to  a  colloid  condition. 

If  the  substance  exists  in  a  number  of  different  physical 
forms,  then  it  is  possible  to  have  a  large  number  of  isocolloids. 
In  the  case  of  water,  in  addition  to  the  vapor  and  liquid  forms, 
there  have  been  four  or  more  different  modifications  of  solid 
ice  recognized.  There  are  some  sixteen  different  colloid 
types  which  have  been  investigated  and  described. 

Suspensoids  and  Emulsoids.  —  In  the  case  of  two  com- 
ponent systems  in  which  the  degree  of  dispersion  is  such  that 
the  disperse  phase  exists  in  the  colloid  state,  the  sols  are 
termed  suspensoids ;  if  the  disperse  phase  is  liquid,  the  sols 
are  termed  emulsoids.  These  are  synonymous  with  the  two 
classes  of  sols  termed  lyophobic  and  lyophilic  colloids.  Since 
the  classifications  are  based  upon  the  degree  of  dispersion,  it 
is  evident  that  the  lyophobic  colloids  approach  on  one  side 
suspensions  in  liquid-solid  systems,  while  the  lyophilic  col- 
loids approach  emulsions  in  liquid-liquid  systems ;  and  on 
the  other  hand  they  both  approach  very  closely  to  the 
molecular  dispersion  or  the  condition  of  true  solutions. 

In  this  connection  it  is  interesting  to  note  that  under  cer- 
tain conditions  we  have  the  transition  of  liquids  to  solids  and 
vice  versa;  so,  too,  in  the  colloid  state  it  is  possible  for  a 
phase  to  pass  from  a  solid  to  a  liquid  or  a  liquid  to  a  solid. 
Under  proper  conditions  certain  emulsoids  may  be  made 
to  precipitate  as  a  solid.  We  then  have  the  transition  of  an 
emulsoid  to  a  suspensoid  and  the  subsequent  enlargement 


COLLOID   CHEMISTRY  447 

of  the  particles,  so  that  we  may  eventually  have  a  suspension 
with  the  final  precipitation,  or  it  may  even  coagulate  without 
assuming  the  microscopic  dimensions.  The  transition  of 
suspensions  to  emulsions  and  vice  versa  is  also  familiarly 
known,  as  in  concentrated  alcoholic  solutions  of  rosin  to  which 
a  little  water  has  been  added.  These  phenomena  have  led 
many  to  suggest  that  in  the  condensation  of  molecular  dis- 
persion we  have  the  formation  of  droplets,  i.e.  the  liquid 
phase,  which  changes  to  the  solid  phase  ;  and  further,  that  in 
all  processes  of  crystallization  or  separation  of  the  solid 
phase  the  liquid  phase  is  first  formed  as  an  intermediate 
transitional  stage.  In  some  cases  this  transition  stage  exists 
for  a  very  short  time,  while  in  other  cases  it  exists  for  an  ap- 
preciable time  —  days,  in  many  cases. 

Crystallization  or  Vectoriality.  —  That  certain  molecular 
disperse  phases  condense  and  eventually  separate  into 
crystalline  masses  indicates  that  there  is  a  definite  molec- 
ular arrangement  of  the  molecules  in  space.  The  stage  of 
the  condensation  process  at  which  these  vectorial  properties 
manifest  themselves  is  shown  to  be  while  the  phase  is  still 
liquid,  as  a  number  of  liquids  are  known  to  manifest  the 
vectorial  properties  which  characterize  them  as  crystals. 
We  have  Lehmann's  extensive  researches  in  confirmation  of 
the  vectorial  character  of  liquids.  Von  Weimarn  even  be- 
lieves vectoriality  is  manifested  by  gaseous  substances  and  in 
addition  has  presented  evidence  which  he  considers  to  be 
direct  proof  of  the  vectoriality  of  the  colloid  phases.  In  the 
case  of  colloid  iodine  and  certain  colloid  dyes,  L.  Pelet  and 
Wild  claim  to  have  observed  the  fusion  of  ultramicroscopic 
particles  which  assumed  definite  crystalline  shapes.  W. 
Ostwald  says,  "  The  precipitation  of  the  insoluble  from 
liquids  seems  always  to  occur  primarily  in  the  form  of  drop- 
lets, that  is,  in  the  state  of  an  under-cooled  liquid,"  and  Wo. 
Ostwald  concludes,  "It,"  therefore,  seems  possible  theoreti- 
cally that  a  development  of  crystals  may  take  place  in  that 


448  PHYSICAL   CHEMISTRY 

the  '  crystal  embryos  '  are  at  first  liquid  and  only  later  become 
solid  as  they  enlarge  because  of  a  '  progressive  '  coalition  of 
molecularly  dispersed  particles." 

Coagulation.  —  The  degree  of  dispersion  of  colloids  can  be 
changed  by  a  variety  of  methods  and  to  such  an  extent  that 
the  disperse  phase  may  become  a  mere  suspension  and 
eventually  separate.  Then,  too,  from  suspensions  and  emul- 
sions the  disperse  phase  can  be  caused  to  deposit  as  a  solid 
or  liquid  phase,  and  thus  resembles  the  precipitate  obtained 
from  colloid  solutions.  The  separated  phase  may  be  a  granu- 
lar precipitate,  may  be  flocculent  or  gelatinous,  or  the  whole 
mass  may  set  to  jelly.  Depending  upon  the  particular  form 
assumed,  various  terms  have  been  loosely  applied  to  the 
phenomenon  of  separation  —  such  as  coagulation,  precipita- 
tion, flocculation,  gelatinization,  setting,  etc. 

Among  a  few  of  the  methods  by  which  this  phenomenon 
may  be  brought  about  we  have :  change  in  temperature ; 
change  in  concentration ;  agitation,  including  centrifuging  ; 
addition  of  electrolytes ;  and  addition  of  non-electrolytes. 

If  gelatin  is  dissolved  in  water  and  this  solution  is  allowed 
to  cool,  it  will  set  to  a  firm  jelly.  On  adding  more  water  and 
warming,  the  mass  again  becomes  liquid,  and  we  have  the 
gelatin  redissolved.  That  is,  the  process  is  reversible.  If, 
however,  a  solution  of  colloid  silicic  acid  is  caused  to  gelati- 
nize, one  way  to  get  this  again  into  the  form  of  a  colloid  solu- 
tion is  to  fuse  the  precipitate  with  sodium  hydroxide,  dissolve 
the  mass  in  water,  decompose  with  acid,  place  in  a  dialyzer, 
and  remove  the  salt.  Colloids  of  this  class  are  designated 
irreversible.  Whether  a  colloid  system  is  reversible  or  irre- 
versible is  determined  many  times  by  the  treatment  to  which 
the  system  is  subjected,  and  Zsigmondy  suggests  that  this 
classification  should  be  confined  to  the  one  factor  of  desicca- 
tion at  ordinary  temperature.  That  is,  a  reversible  colloid 
is  one  which  on  addition  of  the  original  solvent  or  disperse 
means  to  the  precipitated  disperse  phase  will  cause  the  forma- 


COLLOID   CHEMISTRY  449 

tion  of  the  original  dispersoid  system.  According  to  this, 
then,  most  colloid  metals,  hydroxides,  and  sulphides  are 
irreversible,  while  among  the  reversible  colloids  may  be  listed, 
molybdic  acid,  gum  arabic,  dextrin,  and  most  albumens. 

Addition  of  Electrolytes.  —  In  general,  it  may  be  stated 
that  electrolytes  when  added  to  colloid  solutions  cause  the 
coagulation  of  the  disperse  phase.  The  amount  of  the  elec- 
trolyte required  to  produce  precipitation  in  the  case  of  irre- 
versible colloids  is  usually  very  small,  while  it  is  necessary 
to  add  large  quantities  to  the  reversible  colloids,  as  they  are 
not  so  sensitive. 

A  concentration  of  24  per  cent  of  ammonium  sulphate  is 
required,  according  to  Kauder,  before  any  precipitation  of 
globulins  begins,  and  36  per  cent  is  necessary  for  complete 
precipitation.  This  method  of  salting  out  is  employed  in 
separating  many  organic  colloids,  particularly  the  emulsoids 
such  as  albumens,  etc.  A  35  per  cent  solution  of  ammonium 
sulphate  when  added  to  blood  serum  separates  the  globulins, 
but  a  concentration  of  70-80  per  cent  is  necessary  for  the  pre- 
cipitation of  the  albumens.  The  kind  of  salt  employed  has 
a  marked  effect,  and  it  has  been  shown  that  the  precipitation 
of  pure  albumen  increases  for  the  cations  in  the  order  NH4, 
K,  Na,  Li,  and  for  the  anions  in  the  order  CNS,  I,  Br,  NO3, 
Cl,  C2H3O2,  and  SO4. 

It  has  been  shown  by  Linder  and  Picton  that  minute  quan- 
tities of  electrolytes  cause  the  coagulation  of  most  irrevers- 
ible inorganic  colloids,  and  this  has  been  confirmed  by 
numerous  workers.  Benton  gives  the  following  classifica- 
tion of  colloid  solutions  and  suspensions : 

I.   Anionic,  solutions  in  water  in  which  the  particles  move  toward  the 
anode,  i.e.  are  negatively  charged  : 

1.  The  sulphides  of  arsenic,  antimony,  and  cadmium. 

2.  Solutions  of  platinum,  silver,  and  gold. 

3.  Vanadium  pentoxide. 

4.  Stannic  acid  and  silicic  acid. 

5.  Aniline  blue,  indigo,  molybdena  blue. 


450  PHYSICAL   CHEMISTRY 

6.  Iodine,  sulphur,  shellac,  rosin. 

7.  Starch,  mastic,  caramel,  lecithin. 

II.   Cationic,  solutions  in  water  in  which  particles  move  toward  the 
cathode,  i.e.  are  positively  charged  : 

1.  The  hydrates  of  iron,  chromium,  aluminium,  copper,  zirconium, 
cerium,  and  thorium. 

2.  Bredig  solutions  of  bismuth,  lead,  iron,  copper,  and  mercury. 

3.  Hoffmann  violet,  Magdala  red,  methyl  violet,  rosaniline  hydro- 
chloride,  and  Bismarck  brown. 

4.  Albumen,  haemoglobin,  and  agar. 

From  the  fact  that  the  particles  of  the  disperse  phase  may 
be  either  positively  or  negatively  charged  Hardy  formulated 
a  general  statement,  which  is  also  known  as  the  Linder- 
Picton-Hardy  Law,  expressed  as  follows :  The  most  active 
precipitants  are  those  ions  carrying  a  charge  of  opposite  sign 
to  that  carried  by  the  particles  of  the  disperse  phase.  The 
precipitating  power  also  increases  greatly  with  tne  valency 
of  the  ion. 

The  coagulative  power  of  electrolytes,  that  is,  the  recipro- 
cal of  the  concentration  in  moles  per  liter  necessary  to  coagu- 
late a  given  solution,  increases  greatly  with  the  valency  of  the 
ion.  Whetham  points  out  that  in  order  to  produce  coagula- 
tion of  a  sol  a  certain  minimum  electrostatic  charge  has  to 
be  brought  into  contact  with  the  particle  constituting  the  dis- 
perse phase.  Through  the  velocity  of  these  particles  the 
number  of  collisions  results  in  the  union  of  the  charges.  As 
these  charges  are  proportional  to  the  valency  of  the  ions  and 
their  number  proportional  to  the  conductance  of  the  solu- 
tion, the  coagulative  power  of  the  electrolyte,  as  Linder 
and  Picton  showed,  depends  upon  the  electrical  conductance 
of  the  solution.  An  equal  number  of  electrical  charges  would 
be  obtained  from  two  trivalent  ions,  from  three  divalent  ions, 
and  from  six  monovalent  ions. 

Burton  determined  the  velocity  under  electrical  pressure 
of  the  positively  charged  copper  of  a  copper  colloid  solution 
and  the  effect  on  the  same  when  solutions  of  electrolytes  of 


COLLOID   CHEMISTRY 


451 


different  concentrations  were  added.     Some  of  his  results 
are  given  in  Table  LXXXVII. 

TABLE  LXXXVII 


SOLUTION 

CONCEN- 
TRATION 

MlLLI-MOLES 

PER  LITER 

VELOCITY 

AT  l8°X 

io-5 

SOLUTION 

CONCEN- 
TRATION 

MlLLI-  MOLES 

PER  LITER 

VELOCITY 

AT  l8°X 

io-» 

KC1         i 

0 

+  24.9 

K2SO4               I 

0 

25-4 

2 

17 

^5-7 

2 

7-7 

25-3 

3 

38 

26.2 

3 

19.2 

24.0 

4 

74 

22.8 

4 

384 

21.8 

5 

154 

I8.7 

5 

96.0 

144 

6 

i53-o 

o.o 

K3PO4     i 

o 

25-4 

K6(FeCN6)2   i 

0 

30.4 

2 

3-6 

21.5 

2 

3-55 

14.0 

3 

7.2 

16.8 

3 

7-15 

3-8 

4 

14.4 

3-4 

4 

10.7 

I.O 

5 

21.6 

-4.8 

5 

14-3 

-  i-5 

The  addition  of  Cl~  does  not  coagulate  the  copper,  and  even 
high  concentrations  of  SO4~~  do  not  have  much  effect  on  dis- 
charging the  colloid  particles ;  but  when  trivalent  ions,  either 
PO4  or  (FeCN6)  ,  are  introduced  there  is  a  marked 
change  at  small  dilutions,  relatively  a  small  amount  pro- 
ducing the  coagulation.  The  trivalent  ions  have  the  most 
marked  effect,  and  Burton  concludes  "  that  the  velocity 
results  indicate  that  the  ratios  of  the  powers  of  various  acid 
ions  to  reduce  the  velocity  of  the  copper  particles  are  not  very 
far  removed  from  the  observed  ratios  of  the  powers  of  the 
same  ions  to  produce  coagulation."  This  confirms  Linder 
and  Picton's  work  on  the  coagulation  of  a  colloid  solution 
of  arsenious  sulphide  by  equivalent  solutions  of  monovalent, 
divalent,  and  trivalent  cations,  their  coagulative  power  being 
in  the  ratio  1:35:  1023.  This  agrees  with  Schultze's  i :  30  : 
1650,  and  Whetham's  theoretical  ratio,  1:32:  1024. 


452  PHYSICAL   CHEMISTRY 

Cataphoresis  and  Endosmose.  —  We  have  seen  that  when 
suspensions,  emulsions,  and  colloid  solutions  are  subjected  to 
electrical  pressure,  the  disperse  phase  wanders  to  one  of  the 
poles,  which  shows  that  these  particles  possess  an  electric 
charge.  This  phenomenon  is  known  as  cataphoresis  and  is 
the  reverse  of  endosmose,  which  denotes  the  passage  of  the 
liquid  along  the  walls  of  the  tube  under  electrical  pressure. 
We  could  imagine  the  particles  of  the  disperse  phase  to  be  so 
numerous  as  to  form  practically  a  continuous  cellular  struc- 
ture such  as  in  the  fine  unglazed  china  where  the  tubes  are 
of  microscopic  size.  The  disperse  phase  would  then  be  sta- 
tionary and  might  be  considered  the  disperse  means,  when  the 
liquid  would  then  become  the  disperse  phase  and  would 
move  under  the  electrical  pressure  to  which  it  would  be 
subjected. 

Effect  of  Medium.  —  The  effect  of  the  medium  may  be 
well  shown  by  a  few  typical  examples.  In  acid  solution  al- 
bumen is  positively  charged,  while  in  neutral  solutions  there 
is  practically  no  motion  under  the  electrical  pressure ;  and  if 
the  solution  is  alkaline,  the  particles  are  negatively  charged. 

Platinum  in  chloroform  was  found  by  Billitzer  to  be  posi- 
tively charged  and  in  water  negatively  charged.  The  addi- 
tion of  certain  electrolytes  to  metallic  hydrosols  even 
changes  the  sign  of  the  charge  carried  by  the  particles  in 
solution. 

Benton  prepared  Bredig  solutions  of  lead,  tin,  and  zinc 
in  alcohol,  in  which  all  were  positively  charged,  while  bro- 
mine was  negatively  charged  in  the  same  solvent.  In 
methyl  alcohol  Bredig  solutions  of  lead,  bismuth,  iron,  copper, 
tin,  and  zinc  were  found  to  be  positively  charged,  while  in 
ethyl  malonate  solutions  platinum,  silver,  and  gold  were 
negatively  charged.  In  aqueous  solutions  of  starch,  gelatin, 
agar,  and  silicic  acid  the  charges  on  the  particles  could  hardly 
be  detected,  as  there  was  such  a  slight  movement  of  them 
when  subjected  to  electrical  pressure. 


COLLOID   CHEMISTRY  453 

Adsorption.  —  In  the  precipitation  of  colloids  by  elec- 
trolytes it  is  found  in  many  cases  that  the  electrolyte  also 
appears  with  the  precipitated  colloid.  By  the  process  of 
washing,  it  cannot  be  removed  from  the  gel.  We  say  that 
the  electrolyte  has  been  adsorbed.  When  a  colloidal  solu- 
tion of  arsenious  sulphide  is  coagulated  by  BaCl2,  it  is  found 
that  there  is  considerable  barium  present  in  the  gel,  while  the 
concentration  of  the  chlorine  in  the  solution  remains  con- 
stant. It  has  further  been  shown  that  the  quantities  of  dif- 
ferent metals  which  are  adsorbed  by  any  particular  colloid 
are  in  the  same  ratio  to  one  another  as  their  chemical  equiv- 
alents. These  adsorbed  metallic  constituents  cannot  be 
removed  by  washing  but  can  be  removed  by  displacement 
with  other  elements  and  in  equivalent  quantities.  This  is, 
however,  a  mass  action  phenomenon,  for  the  process  of  sub- 
stitution may  be  reversed  by  changing  the  relative  masses 
of  the  reacting  substances.  Linder  and  Picton  found  that 
when  calcium  chloride  was  employed,  the  calcium  adsorbed 
by  the  gel  could  be  replaced  by  cobalt ;  and  if  a  salt  of  cobalt 
was  employed  as  the  coagulant,  the  cobalt  adsorbed  by  the 
gel  could  be  replaced  by  calcium. 

From  such  experiments  as  these  it  has  been  concluded  that 
chemical  reactions  take  place  and  the  resulting  precipitate  is 
a  true  chemical  compound.  In  the  case  of  many  substances 
whose  degree  of.  dispersion  is  less  than  that  of  the  disperse 
phase  in  colloid  solutions,  wherein  we  have  mere  suspension, 
suspensions  such  as  clay  manifest  the  same  phenomenon. 
While  in  the  case  of  many  precipitates  in  analytic  work  we 
have  the  electrolyte  adsorbed  by  the  precipitate,  as  in  the 
case  of  precipitation  of  BaSO4,  which  adsorbs  BaCl2  readily, 
and  in  the  precipitation  of  zinc  and  of  manganese  with  the 
members  of  the  preceding  group,  as  well  as  in  numerous  other 
examples  wherein  the  precipitates  are  washed  free  from 
impurities  with  difficulty.  When  two  colloids  of  opposite 
signs  electrically  are  mixed,  the  gel  resulting  will  be  a  mixture 


f 

454  PHYSICAL   CHEMISTRY 

of  the  two,  the  composition  depending  upon  the  original 
relative  concentration  of  the  colloid  solutions.  For  exam- 
ple, when  a  colloidal  solution  of  ferric  hydroxide,  which  is 
electrically  positive,  is  mixed  with  a  colloid  solution  of  arse- 
nious  sulphide,  which  is  electrically  negative,  the  resulting  gel 
is  a  mixture  of  the  two,  and  by  varying  the  original  concen- 
tration of  the  colloid  solutions  gels  of  continuously  varying 
composition  can  be  obtained,  and  when  the  electrical  charges 
are  just  neutralized  complete  precipitation  takes  place. 
Some  investigators,  including  van  Bemmelen,  even  go  so  far 
as  to  consider  many  of  the  gelatinous  precipitates,  such  as 
the  hydroxides  of  iron,  aluminium,  etc.,  as  oxides  of  the 
metals  which  have  absorbed  water,  i.e.  they  are  adsorption 
compounds.  Many  other  substances  which  have  been  con- 
sidered as  true  chemical  compounds  are  now  held  to  be  ad- 
sorption products.  For  example,  purple  of  Cassius  (formally 
termed  aurous  stannous  stannate)  is  considered  by  Zsig- 
mondy  to  be  an  adsorption  compound  of  colloidal  gold  and 
colloidal  stannic  acid. 

From  the  foregoing  we  have  seen  that  these  adsorption 
compounds  have  been  considered  as  true  chemical  com- 
pounds, and  it  is  evident  that  we  may  also  be  dealing  with 
solid  solutions ;  but  the  tendency  at  present  is  to  consider 
these  products  as  the  result  of  surface-tension  phenomena, 
and  they  are  designated  as  surface-tension  condensation 
products. 

Adsorption  by  charcoal  is  very  pronounced  and  is  com- 
monly known  in  its  use  for  the  removal  of  the  last  traces  of 
gases  in  the  production  of  a  high  vacuum,  for  the  purification 
of  sirups  and  numerous  other  liquids  by  the  removal  of  the 
coloring  matter,  as  well  as  for  the  adsorption  of  metals  from 
their  aqueous  solutions  —  all  of  which  constitute  many  im- 
portant technical  processes.  In  the  case  of  vapors  of  iodine, 
the  amount  adsorbed  is  proportional  to  the  vapor  pressure, 
and  a  final  state  of  equilibrium  results. 


COLLOID   CHEMISTRY  455 

The  amount  of  solute  adsorbed  is  proportional  to  the  sur- 
face of  the  adsorbent  and  is  expressed  by  the  following 
i 

equation  :    —  =  a  cn,  in  which  %  is  the  weight  of  the  substance 
m 

adsorbed,  m  the  weight  of  the  adsorbent,  c  the  volume  con- 
centration after  adsorption,  a  and  -  are  constants.  This 

n 

has  been  confirmed  by  Walker  and  Appleyard,  who  obtained 
for  the  adsorption  of  picric  acid  from  a  o.oi  N  solution  in 
water  and  in  alcohol  by  charcoal  and  by  silk : 

^(charcoal)      water  alcohol 

~ =     7-3  5-2 

-     (silk) 
m 

For  any  substance  the  adsorption  is  proportional  to  the 
specific  surface,  which  is  closely  related  to  the  amount  of 
chemical  change.  Since  all  surface  energies  and  volume 
energies  are  interrelated,  electrical  energy,  which  is  a  surface 
energy,  and  surface  phenomena,  such  as  adsorption,  must  be 
related. 

It  is  assumed  that  at  the  boundary  surface,  solution-solid, 
in  these  heterogeneous  systems  there  is  a  surface  concentration 
different  from  that  within  the  solution,  and  that  the  greater 
the  extension  of  the  solid  surface,  i.e.  of  the  disperse  phase,  the 
greater  becomes  the  concentration  on  it.  From  extensive 
experimental  evidence  Lagergren  has  shown,  by  the  appli- 
cation of  Le  Chatelier's  theorem,  that  depending  upon  the 
change  in  solubility  of  the  solute  with  change  of  pressure  we 
may  have  either  positive  or  negative  adsorption,  and  from 
this  experimental  evidence  it  is  concluded  that  the  surface 
layer  is  in  a  state  of  high  compression,  which  is  due  to  the 
action  of  the  cohesive  forces.  The  heat  evolved  when  in- 
soluble powders  are  wetted  would  be  due  then  to  compres- 
sion of  the  adsorbed  solvent. 


456  PHYSICAL  CHEMISTRY 

The  absolute  surface  of  substances  does  not  consist  of  the 
external  surface  only,  for  all  solids  are  more  or  less  porous  and 
therefore  contain  numerous  capillary  tubes  which  give  the 
mass  a  cellular  structure,  increase  greatly  the  absolute  sur- 
face as  well  as  the  specific  surface,  and  likewise  the  adsorbing 
power  of  the  adsorbent.  So  this  cellular  or  honeycomb  struc- 
ture, which  is  attributed  by  some  authors  to  gels  in  general, 
is  also  assumed  for  all  very  finely  divided  substances  as  well. 
This  is  manifest  particularly  in  the  case  of  charcoal,  which 
adsorbs  metals  from  aqueous  solutions,  and  in  many  cases 
the  metal  is  completely  removed,  the  solution  becoming 
strongly  acid  while  the  adsorbed  metal  cannot  be  washed  out 
from  the  charcoal.  Not  only  is  this  phenomenon  assumed  to 
be  one  of  adsorption,  but  even  the  formation  (precipitation) 
of  metals  from  metal  ions  need  not  be  considered  primarily 
a  chemical  reaction,  but  is  explained  upon  the  basis  of  the 
highly  porous  character  of  the  substances,  such  as  charcoal. 
In  contact  with  water,  the  adsorbent  becomes  negatively 
charged1  and  the  water  positively  charged,  and  a  metal 
ion  in  attempting  to  diffuse  into  the  body  of  the  charcoal 
will  pass  into  the  capillary  opening  and  may  have  its  electri- 
cal charge  neutralized  by  the  negative  charge  of  the  charcoal 
and  be  deposited  as  the  metal.  This  explanation  is  also  given 
for  the  deposition  of  metals  in  very  fine  cracks  in  glass. 

The  adsorption  of  dyes  by  filter  paper  is  explained  in  a 
similar  manner,  the  fiber  is  negatively  charged  while  the 
water  is  positive,  and  a  positive  sol  will  neutralize  the  charge 
on  the  paper,  will  become  neutral,  and  be  precipitated  on  the 
fiber.  Similarly,  a  negative  dye  would  not  be  precipitated, 
thus  giving  a  method  of  separating  and  distinguishing  them. 
The  same  is  true  of  gels  which  are  themselves  strongly  posi- 

1  Perrin  has  shown  that  for  many  cases  this  is  not  true.  Coehn  states  that  the 
substance  with  the  higher  dielectric  constant  is  positive  against  the  substance  with 
a  lower  value  for  constant.  Hence,  as  water  has  nearly  the  highest  value  known 
(81)  all  other  substances  would  be  electronegative  toward  water.  Also  see  Briggs, 
Jour.  Phys.  Chem.,  21,  198  (1917). 


COLLOID   CHEMISTRY  457 

tive  or  strongly  negative,  and  their  strong  adsorptive  power 
is  attributed  to  this.  The  adsorption  results  in  the  concomi- 
tant decomposition  of  the  adsorbed  salts. 

We  will  not  take  up  Gibbs'  consideration  wherein  he  has 
shown  thermodynamically  that  if  a  dissolved  substance  had 
the  property  of  lowering  the  surface  tension  of  the  solution, 
the  substance  would  exist  at  a  higher  concentration  in  the 
surface  layer  than  in  the  bulk  of  the  solution.  Nor  must  we 
lose  sight  of  the  fact  that  while  many  of  these  attempted  ex- 
planations are  purely  physical,  it  is  possible  to  apply  the  Dis- 
tribution Law  to  them  and  show  that  the  phenomenon  is  of 
the  nature  of  solution,  and  giving  rise  in  other  cases  to  the 
so-called  solid  solution  theory  of  dyeing.  Then,  too,  in 
many  of  these  purely  physical  theories  we  find  no  factors 
which  account  for  the  fastness  of  the  dyes,  a  fact  which 
emphasizes  the  chemical  reaction  between  the  dye  and 
the  fiber  or  the  mordants  employed.  The  same  applies  to 
the  enzyme-action  where  some  kind  of  combination  takes 
place  between  the  enzyme  and  the  substance  upon  which  it 
acts,  thus  demonstrating  their  colloidal  character  and 
their  marked  power  as  adsorbents. 

With  the  increased  dispersion  of  the  disperse  phase  the 
absolute  surface  increases  enormously,  and  since  the  amount 
of  chemical  change  in  unit  time  is  proportional  to  the  absolute 
surface,  we  should  expect  the  reactions  to  occur  much  more 
slowly  when  the  particles  are  coarse  than  when  they  are  very 
fine.  Hydrogen  peroxide  is  decomposed  slowly  when  smooth 
platinum  foil  is  employed,  but  if  this  is  covered  with  plati- 
num black,  which  is  metallic  platinum  in  a  very  fine  state  of 
division,  the  decomposition  is  very  much  more  rapid.  Since 
in  colloidal  systems  we  have  the  disperse  phase  in  a  very  fine 
state  of  division,  the  specific  surface  would  be  large  and  we 
should  expect  the  colloids  to  have  a  very  marked  influence 
upon  the  speed  of  the  chemical  reaction.  Such  is  the  case, 
and  we  have  the  great  increase  in  the  speed  of  the  chemical 


458  PHYSICAL  CHEMISTRY 

reaction  through  the  mere  contact  of  the  finely  disseminated 
colloid.  This  phenomenon  is  designated  catalysis,  and  the 
substance  which  brings  about  this  enormous  change  is  desig- 
nated a  catalyzer.  Bredig  and  his  pupils  have  shown  that  not 
only  are  many  inorganic  substances  in  the  colloidal  state 
capable  of  producing  catalysis,  but  the  same  results  may  also 
be  accomplished  by  the  organic  ferments  termed  enzymes. 

Protective  Colloids  —  One  would  conclude  from  what  has 
been  said  concerning  the  precipitating  effects  of  electrolytes, 
that  in  order  to  have  a  colloid  solution  that  is  stable,  it  would 
be  necessary,  in  the  preparation  of  colloid  solutions  by  chemi- 
cal reaction  and  the  subsequent  removal  of  the  electrolyte 
by  dialysis,  to  remove  all  traces  of  the  electrolytes.  As  a 
general  thing  this  is  true,  but  some  authors  believe  that  these 
minute  traces  are  essential  to  the  formation  of  a  stable  colloid 
solution  and  that  they  have  a  very  pronounced  stabilizing 
effect.  Graham  proved  that  colloid  silicic  acid  solutions  are 
more  stable  the  longer  they  are  dialyzed,  but  it  is  known 
that  colloid  solutions  of  ferric  hydroxide  are  less  stable  if 
all  of  the  hydrochloric  acid  has  been  removed.  Numerous 
workers  have  presented  a  number  of  facts  which  show  that 
both  effects  are  produced,  and  that  even  some  colloids  have  a 
stabilizing  effect  on  other  colloids.  This  is  true  particularly 
in  the  case  of  suspensoids  where  the  stabilizing  agent  is  an 
emulsoid.  This  is  not  due  primarily  to  a  change  in  the 
viscosity  of  the  disperse  means.  Hydrosols  of  metals  usually 
exist  in  very  dilute  solutions,  but  by  the  addition  of  albumen, 
dextrin,  or  starch  very  much  more  concentrated  solutions  can 
be  obtained.  It  is  stated  that  one  milligram  of  gelatin 
will  prevent  the  precipitation  by  sodium  chloride  of  a  liter 
of  colloidal  gold.  Blood  serum  will  do  the  same.  Quincke 
has  shown  the  protective  action  of  gelatin  in  the  system, 
mastic-gelatin-water.  This  is  also  pronounced  in  the  case 
of  suspensions  as  well  as  where  the  protective  action  is  pro- 
duced by  organic  as  well  as  by  inorganic  colloids.  Carey 


COLLOID  CHEMISTRY  459 

Lea's  colloid  silver,  which  is  produced  by  reducing  silver  salts 
with  tartrates,  ferrous  salts,  dextrin,  carmin,  or  such  sub- 
stances, may  be  protected  by  either  an  electrolyte  or  a  col- 
loid, and  a  colloid  silver  content  of  over  90  per  cent  soluble 
in  water  can  readily  be  obtained.  Certain  colloid  silver  solu- 
tions containing  protein  substances  used  in  medicine  contain 
as  high  as  75  per  cent  of  silver  upon  this  basis.  Zsigmondy 
has  devised  a  method  for  the  identification  and  separation 
of  various  proteins,  and  these  have  been  extended  by  the 
work  of  Biltz. 

Physical  Properties.  —  The  change  in  volume  of  colloid 
solutions  with  pressure  is  but  very  little  different  from  that 
of  the  pure  disperse  means  and  also  from  that  of  true  molec- 
ular dispersoids.  Gelatin  at  100°  is  about  10  per  cent  less 
compressible  than  pure  water,  while  a  30  per  cent  solution  of 
KI  according  to  Gilbant  is  even  less  compressible. 

We  have  seen  that  as  the  degree  of  dispersion  increases  the 
specific  volume  (volume  weight)  increases  enormously,  and 
that  at  the  intersurf  ace  contact  there  is  a  marked  condensa- 
tion of  the  disperse  means.  It  has  been  found  that  water 
drops  0.3  mm.  in  diameter  have  a  density  0.5  per  cent 
greater  than  water  in  usual  condition.  So  it  follows  that  the 
density  of  colloid  systems  must  be  greater  than  when  they 
are  in  a  less  dispersed  condition.  Molten  and  compressed 
gold  has  a  density  of  19.33  ;  "that  precipitated  by  oxalic  acid, 
19.49 ;  while  that  precipitated  by  ferrous  sulphate  is  19.55 
to  20.71.  That  is,  the  greater  the  degree  of  dispersion  of  sus- 
pensoids  the  greater  their  density.  In  the  case  of  emulsoids 
this  is  just  as  pronounced.  Quincke  observed  a  decrease 
in  volume  of  more  than  3.5  per  cent  in  the  system  dried  egg- 
albumen-water.  The  density  of  hydrogels  is  decidedly 
greater  than  that  of  the  dry  substance  ;  for  example,  a  50  per 
cent  solution  of  gelatin  gave  an  observed  density  of  1.242, 
whereas  the  calculated  value  was  1.206. 

If  the  volume  of  the  disperse  means,  water,  is  calculated 


460 


PHYSICAL   CHEMISTRY 


after  this  contraction,  it  will  be  found  to  be  much  less  with 
increasing  concentration  of  the  disperse  phase,  as  is  shown  by 
the  following  calculated  value  of  the  volume  of  i  cc.  of  water 
after  contraction : 

In  a  10  per  cent  solution  of  gelatin        0.96069  cc. 

In  a  25  per  cent  solution  of  gelatin         0.93748  cc. 

In  a  50  per  cent  solution  of  gelatin         0.90201  cc. 

The  same  is  true  for  the  starch-water  system ;  the  contrac- 
tion increases  with  the  concentration,  whether  it  be  referred 

to  the  disperse  means  or  to  the 
disperse  phase. 

From  Fig.  93  it  will  be  seen 
that  for  the  suspensoids  such  as 
As2S3  the  density-concentration 
is  a  linear  function,  while  for 
emulsoids  such  as  gelatin  there 
is  a  decided  curve,  which  is  con- 
cave toward  the  concentration 
axis.  As  illustrated  by  the 
curve  for  NaCl,  we  see  that  it 


Concentration 


FIG.  93. 


is  analogous  to  that  for  emulsoids  and  emphasizes  the  simi- 
larity of  the  true  molecular  disperse  systems  and  the  proper- 
ties of  emulsoids.  The  density-concentration  gives  us  a 
means  of  distinguishing  the  two. 

Colligative  Properties  of  Colloid  Solutions.  —  We  have  seen 
in  the  case  of  true  solutions,  i.e.  molecular  dispersed  systems, 
that  the  vapor  pressure  of  the  disperse  means  is  greatly  modi- 
fied by  the  addition  of  the  second  component,  the  disperse 
phase.  The  vapor  pressure  of  the  pure  solvent  is  lowered  by 
the  addition  of  the  solute.  Likewise,  there  is  a  marked  lower- 
ing of  the  freezing  point  and  a  rise  of  the  boiling  point  pro- 
duced by  the  addition  of  the  solute.  The  amount  of  change 
in  the  vapor  pressure,  the  freezing  point,  and  the  boiling 
point  is  proportional  to  the  concentration  of  the  solute,  and 
is  a  function  of  the  molar  concentration. 


COLLOID   CHEMISTRY  461 

The  solute,  i.e.  the  disperse  phase,  is  molecularly  dis- 
persed. In  dilute  solutions  the  changes  of  these  properties 
conform  to  the  laws  of  solutions  which  we  have  previously 
considered,  but  we  have  seen  that  as  the  concentration  of 
the  disperse  phase  (solute)  is  increased  and  the  solutions 
become  concentrated,  abnormal  values  are  obtained  for  the 
data,  for  which  explanations  are  attempted  upon  various 
assumptions,  such  as  association  of  solute  as  well  as  of 
the  solvent,  combination  of  the  solvent  and  solute  (hydra- 
tion),  etc. 

The  measurements  of  the  vapor  pressure,  the  freezing  point, 
and  the  boiling  point  of  colloid  solutions  show  that  these 
properties  of  the  disperse  means  are  but  slightly  if  at  all 
affected  by  the  addition  of  disperse  phase  of  the  degree  of 
dispersion  we  designate  colloid.  Data  from  a  large  number 
of  colloid  solutions  have  been  collected,  and  these  show 
that  the  vapor  pressure,  freezing  point,  and  boiling  point 
are  practically  the  same  as  those  of  the  pure  disperse  means, 
nor  are  they  changed  appreciably  by  a  large  increase  in  the 
concentration  of  the  disperse  phase.  The  slight  change  ob- 
served in  some  cases  is  attributed  to  the  presence  of  impuri- 
ties in  the  materials  used. 

Osmotic  Pressure.  —  In  the  discussion  of  the  osmotic 
pressure  of  true  solutions  we  have  seen  that  by  the  use  of  a 
colloid  septum,  such  as  a  precipitated  copper  ferrocyanide 
membrane,  we  have  a  semipermeable  membrane  which  per- 
mits the  passage  of  the  solvent,  i.e.  of  the  disperse  means. 
The  hydrostatic  pressure  developed  by  the  use  of  such  a 
membrane  in  the  osmotic  cell  we  term  the  osmotic  pressure 
of  the  dispersoid.  It  is  stated  that  the  disperse  means  passes 
through  the  membrane,  diluting  the  solution  contained  in  the 
osmotic  cell.  It  was  not  stated,  however,  just  how  the  dis- 
perse means  "  passed  through  "  the  membrane,  whether  it 
was  due  to  the  sieve-like  character  or  the  selective  solvent 
action  of  the  membrane. 


462  PHYSICAL   CHEMISTRY 

Bancroft  says  : l  "  We  can  get  osmotic  phenomena  in  two 
distinct  ways  depending  on  whether  we  have  a  continuous 
film  or  a  porous  one.  In  the  case  of  a  continuous  film  it  is 
essential  that  the  solvent  shall  dissolve  in  the  membrane  and 
the  solute  shall  not.  Since  the  permeability  is  not  dependent 
on  adsorption,  there  is  no  reason  why  there  should  be  any 
fundamental  difference  between  the  adsorption  of  a  solute 
which  does  pass  through  the  membrane  and  of  one  which 
does  not  pass  through.  If  we  have  a  porous  film,  we  get 
osmotic  phenomena  only  in  case  the  pore  walls  adsorb  the 
pure  solvent  and  the  diameter  of  the  pores  is  so  small  that 
the  adsorbed  film  of  the  pure  solvent  fills  the  pores  full. 
Under  these  circumstances  the  dissolved  substance  cannot 
pass  through  the  pores.  On  the  other  hand,  if  the  dissolved 
substance  can  pass  through  the  membrane,  it  must  be  ad- 
sorbed by  the  latter.  There  is  therefore  a  fundamental  dif- 
ference between  a  solute  which  does  pass  through  a  porous 
membrane  and  one  that  does  not  in  that  the  first  is  adsorbed 
by  the  membrane  and  the  second  is  not." 

If  colloid  solutions  are  employed  in  an  osmotic  cell,  a  small 
osmotic  pressure  is  developed ;  but  the  question  arises  as  to 
whether  this  small  value  may  not  be  due  to  the  impurities 
in  the  colloid  solutions.  For  it  will  be  remembered  that  by 
the  process  of  dialysis  it  is  exceedingly  difficult  to  remove 
all  of  the  electrolytes  from  them,  owing  to  the  marked  adsorp- 
tive  power  of  the  colloid  and  also  because  of  the  stabilizing 
power  of  certain  electrolytes.  Numerous  efforts  have  been 
made  to  determine  whether  the  osmotic  pressure  developed 
was  really  due  to  the  colloid  or  to  the  impurities  present. 
This  was  accomplished  by  determining  the  electrolyte  con- 
tent of  the  colloid  and  then  introducing  the  same  content  into 
the  outer  liquid  so  as  to  have  the  concentration  of  the  elec- 
trolyte the  same  within  the  cell  as  on  the  outside,  thus  elim- 
inating the  osmotic  effect  due  to  the  electrolyte.  Then  the 
1  Jour.  Phys.  Chem.,  21,  450  (1917). 


COLLOID   CHEMISTRY 


463 


value  obtained  would  be  the  experimental  value  of  the  osmotic 
pressure  of  the  colloid  itself. 

Factors  Affecting  Osmotic  Pressure.  —  The  values  ob- 
tained vary  greatly,  depending  upon  the  method  of  prepa- 
ration of  the  dispersoid  and  its  previous  treatment.  The  os- 
motic pressure  of  molecularly  disperse  systems  soon  reaches 
a  maximum  and  remains  at  that  value,  whereas  the  osmotic 
pressure  of  colloid  systems  reaches  a  maximum  and  then  a 
marked  decrease  takes  place.  Shaking  or  stirring  the  solu- 
tion has  a  marked  effect  upon  the  osmotic  pressure.  In  fact, 
the  variability  is  a  marked  distinction  between  colloid  solu- 
tions and  molecular  dispersoids  and  is  attributed  to  a  change 
taking  place  in  the  dispersion  of  the  colloid  system  resulting 
in  different  states  of  aggregation  and  a  change  in  viscosity. 
This  is  true  particularly  in  emulsoids. 

In  molecular  dispersoids  Pfeffer  showed  that  the  osmotic 
pressure  is  proportional  to  the  concentration  of  the  disperse 
phase  and  also  to  the  absolute  temperature,  but  in  the  case 
of  colloid  solutions  there  is  no  such  regularity  manifest. 
According  to  Martin  and  Bayliss 
the  osmotic  pressure  of  albu- 
men, haemoglobin,  and  congo 
red  varies  directly  with  the  ab- 
solute temperature.  For  gela- 
tin solutions  Moore  and  Roof 
found  that  the  osmotic  pressure 
increased  much  faster  than  the 
absolute  temperature.  Duclaux 
vshowed  that  the  osmotic  pres- 
sure decreased  with  the  increase 
of  temperature.  The  same  marked  irregularities  are  mani- 
fest with  reference  to  the  relation  between  the  osmotic  pres- 
sure and  the  concentration,  —  the  value  of  the  ratio  of  the 
osmotic  pressure  to  the  concentration  is  not  a  constant. 
This  is  well  illustrated  in  Fig.  94.  Congo  red  gives  nearly  a 


sol 


Concentration 


FIG.  94. 


464 


PHYSICAL   CHEMISTRY 


constant  value  for  this  ratio,  iron  hydroxide  sol  gives  a  marked 
increase  in  the  values  of  the  ratio  with  the  increase  in  concen- 
tration, while  in  the  case  of  haemoglobin  we  have  a  decided  de- 
crease. The  laws  of  solutions  as  developed  from  a  considera- 
tion of  the  molecular  dispersoids  do  not  appear  to  be  valid  for 
colloid  systems,  for  the  attempt  to  apply  them  does  not  seem 
to  be  any  more  successful  than  in  the  case  of  osmotic  pressure, 
which  apparently  demonstrates  that  we  are  not  justified  in  ap- 
plying the  laws  of  molecular  dispersoids  to  the  colloid  systems. 
The  addition  of  substances  to  colloid  systems  manifests 
the  same  erratic  change  in  the  osmotic  pressure  as  we  noticed 
with  reference  to  the  change  in  the  concentration  of  the  dis- 
perse phase.  In  molecular  disperse  systems  the  addition  of 
another  substance  has  an  additive  effect.  The  osmotic  pres- 
sure of  a  highly  dispersed  congo  red  sol  was  found  by  Bayliss 
to  be  207  mm.  By  replacing  the  water  about  the  cell  with 
water  saturated  with  carbon  dioxide,  the  osmotic  pressure 
was  120  mm.  The  addition  of  alkali  usually  causes  an  in- 
crease in  the  osmotic  pressure  in  certain  cases,  but  in  the 
case  of  egg  albumen  the  osmotic  pres- 
sure is  always  diminished. 

The  disperse  means  enters  the  os- 
motic cell  and  there  is  the  increased 
volume  resulting  in  the  so-called  os- 
motic effect,  or  as  some  authors  pre- 
fer, the  "  pseudo-osmotic  "  pressure. 
This  pseudo-osmotic  imbibition  is 
not  unlike  the  swelling  phenomena  in 
a  solid  colloid. 

In  Fig.  95  is  given  the  effect  of  acid 


00010          ooeo         00 jo 
Normal    Concentration 


FIG.  95. 


and  alkali  on  the  pseudo-osmotic  pressure  of  a  1.5  per  cent 
gelatin  sol  as  determined  by  Lillie,  while  in  Fig.  96  is  illus- 
trated the  influence  of  acid  and  alkali  on  the  swelling  of  gelatin 
according  to  the  experiment  of  Wo.  Ostwald.  The  analogy  is 
very  pronounced. 


COLLOID   CHEMISTRY 


465 


The  relation  between  the  viscosity  of  albumin  sol  as  af- 
fected by  the  addition  of  acid  and  of  alkali  as  shown  in  Fig. 
97,  according  to  Pauli,  and  the  change  of  the  pseudo-osmotic 
pressure  according  to  Lillie,  is  very  manifest  by  the  shape,  of 
curves.  The  increase  in  internal  friction 
(viscosity)  corresponds  to  a  decrease  in  the 
pseudo-osmotic  pressure,  and  this  holds 
completely  not  only  in  the  case  of  viscosity 
and  osmosis,  but  also  for  gelatinization, 
and  as  wre  have  seen  for  swelling  as  well. 
We  are  then  dealing  with  complex  phe- 
nomena which  are  most  intimately  con- 
nected with  one  another. 

The  addition  of  salts  to  sols  of  albumin 
and  of  gelatin  has  been  found  by  Lillie  to 
decrease-  the  osmotic  pressure.    The  mag- 
nitude of  the  decrease  is  less  in  the  case  of  normal  salts  of  the 
alkali  metals  than  in  the  case  of  the  alkaline  earth  metals, 
while  the  salts  of  the  heavy  metals  produce  the  most  marked 
decrease  in  the  osmotic  pressure.     The  acid  or  alkaline  char- 


v 


0009     013  '  036 

formal    Concentration 


aooi  .ooz  .003 

Normal     Concentration 

FIG.  97  a. 


Normal  Concentration 

FIG.  97  b. 


acter  of  a  colloid  system,  as  we  have  just  seen,  not  only  affects 
the  pseudo-osmotic  pressure  but  also  the  viscosity  of  the 
colloid  system. 

The    Brownian    Movement.  —  The   English   botanist   R. 
Brown  (1827)  observed  under  the  microscope  that  particles 


466  PHYSICAL   CHEMISTRY 

if  not  too  large  are  always  in  rapid  motion.  Picton  observed 
these  movements  in  the  microscopically  visible  particles  in 
colloid  metallic  sulphide  solutions,  and  Zsigmondy  shows  it 
to  be  very  pronounced  under  the  ultramicroscope.  This 
is  termed  the  Brownian  movement.  The  particles  recog- 
nizable in  all  dispersoids  manifest  this  movement  if  they  are 
not  too  large  and  if  the  disperse  means,  which  may  be  either 
liquid  or  gaseous,  does  not  offer  too  much  resistance.  The 
upper  limit  in  size  of  particles  is  about  o.oi  /A/A  in  diameter. 
The  movements  of  these  larger  particles,  which  are  very 
small,  are  spontaneous  and  continuous  and  of  a  trembling  or 
vibratory  kind  and  in  a  curved  path.  With  increased  dis- 
persity  the  motion  is  translatory  in  a  zigzag  fashion  and 
Zsigmondy  described  it  as  "  dancing,  hopping,  and  skipping," 
as  well  as  "  translatory  and  progressive." 

The  viscosity  of  the  disperse  phase  has  a  marked  effect  on 
the  Brownian  movement.  The  increase  in  temperature 
accelerates  the  Brownian  movement  and  also  decreases  the 
viscosity  of  the  disperse  means.  This  has  been  investigated 
extensively  by  Seddig,  who  concludes  that  the  move- 
ment of  the  particles,  the  amplitude  A,  is  dependent  on 
the  temperature  and  expressed  the  relation  as  follows: 


A.*VJ, 

in  which  17  is  the  viscosity ;  or  A2  =  k  — ,  which  states  that 

the  path-length  squared  is  directly  proportional  to  the  ab- 
solute temperature  and  inversely  proportional  to  the  vis- 
cosity of  the  liquid.  Svedberg's  law  (Arj  =  k)  applied  to 
this  gives  A2rj  =  kT  or  A  •  Arj  =  kT  and  since  At]  =  k,  we 
have  A  =  k\  T,  which  states  that  when  the  viscosity  is  con- 
stant the  path-length  is  directly  proportional  to  the  absolute 
temperature. 

A  very  fine  powder  when  placed  in  water  becomes  coated 


COLLOID   CHEMISTRY  467 

with  the  disperse  means  and  soon  becomes  uniformly  dis- 
tributed throughout  the  water,  thus  showing  that  the 
Brownian  movement  overcomes  the  action  of  gravity. 
Perrin  showed  that  mastic  dispersoids  under  the  influence 
of  gravity  become  stratified.  This  is  general,  and  he  con- 
cludes that  in  the  case  of  the  larger  particles  the  downward 
component  in  the  irregular  motion  of  the  particles  is  aug- 
mented and  previous  uniform  distribution  results  in  the  ac- 
cumulation of  the  particles  at  the  bottom. 

Since  electrolytes  cause  the  coagulation  of  the  disperse 
phase  we  should  expect  that  the  addition  of  electrolytes  to 
colloid  systems  would  have  a  marked  influence  on  the  Brown- 
ian movement.  On  adding  N/io  NaOH  to  caoutchouc  juice 
the  movement  of  the  gutta-percha  particles  was  decreased 
to  one  half  of  their  original  rate,  while  N/io  HC1  reduced  the 
motion  to  only  about  one  ninth  of  its  original  value.  The 
original  path  length  was  0.62/1/1,  while  in  the  alkaline  solu- 
tion it  was  0.3  /A/A,  and  in  the  acid  solution  it  had  decreased 
to  0.07  /A/A.  Schulze  states  that  the  motion  of  the  particles 
in  opalescent  liquids  is  caused  to  cease  by  the  addition  of 
small  quantities  of  alum,  lime,  and  acids  with  clumping,  but 
in  some  cases  the  retardation  of  the  Brownian  movement 
may  occur  without  clumping,  particularly  in  the  more  highly 
dispersed  systems.  Although  the  Brownian  movement  will 
not  prevent  the  stratification  of  the  larger  sized  particles,  it 
is  considered  as  one  of  the  chief  stabilizing  factors  of  sols. 
Perrin  by  observing  the  rate  of  fall  of  a  cloud  of  gamboge 
particles  under  the  influence  of  gravity  was  able  to  deter- 
mine the  number  of  particles  per  unit  volume.  By  applying 
Stoke 's  Law  of  moving  particles  through  a  medium,1  know- 

1  The  velocity  of  a  particle  is  proportional  to  the  square  of  its  radius  and 
inversely  proportional  to  the  viscosity  of  the  medium.  Expressed  mathemati- 
cally it  is  v  =  -  Pl  ~  p  gr2,  where  v  is  the  velocity,  pi  the  density  of  the  particle,  P 

9      "Q 

the  density  of  the  liquid,  >?  the  viscosity,  g  the  gravitational  constant  and  r  the 
radius  of  the  particles. 


468  PHYSICAL  CHEMISTRY 

ing  the  total  mass,  the  viscosity,  the  density  of  the  particles 
in  the  solid  form  and  also  in  the  emulsion,  he  was  able  to 
calculate  the  diameter  of  the  particles  as  well  as  the  Avoga- 
dro  constant,  N,  which  is  the  number  of  parts  in  one  gram- 
equivalent  of  the  disperse  phase.  The  mean  value  for  N 
he  found  to  be  70.0  X  io22.  With  other  emulsions  Perrin 
has  repeated  his  experiments  and  obtained  the  value  68  X  io22. 
Utilizing  the  mathematical  deductions  of  Einstein,  who  as- 
sumed that  the  Brownian  movement  is  due  to  the  impacts 
of  the  molecules  of  the  liquid  on  the  particle,  the  value 
obtained  is  68.6  X  io22 ;  from  which  he  concluded  that  there 
is  no  essential  difference  between  these  particles  and  mole- 
cules, thus  confirming  the  kinetic  theory  of  Brownian 
movement. 

Applications  of  Colloid  Chemistry.  —  The  phenomena  of 
colloid  chemistry  which  we  have  been  considering  include 
adsorption,  surface  tension,  surface  concentration,  diffusion, 
etc.  These  factors  control  our  so-called  physical  and  chemi- 
cal reactions.  The  applications  of  the  principles  embodying 
the  phenomena  are  so  broad  in  scope  that  they  include  prac- 
tically all  of  the  principal  departments  of  chemistry.  Since 
colloid  chemistry  deals  with  all  degrees  of  dispersion  in  a 
system  except  that  designated  as  molecular  dispersion,  the 
domain  of  colloid  chemistry  is  practically  coextensive  with  and 
comprises  most  of  the  industrial  applications  of  chemistry. 
The  list  of  industries  which  utilize  the  applications  of  these 
principles  includes  most  of  the  commercial  applications  of 
chemistry,  among  which  may  be  mentioned  the  wide  field  of 
biological  chemistry,  agriculture,  plastics,  ceramic  industry, 
dyeing,  tanning,  rubber,  sanitation,  soap,  photography,  and 
metallurgy.  It  is  beyond  the  scope  of  our  presentation  to 
consider  these  in  detail,  and  we  shall  only  refer  to  the  appli- 
cation of  the  principles  of  colloid  chemistry  to  the  new  metal- 
lurgical process  of  ore  flotation.  For  a  comprehensive  con- 
sideration of  the  other  industrial  applications  of  colloid 


COLLOID   CHEMISTRY  469 

chemistry  reference  may  be  had  to  the  current  periodical 
literature,  and  to  the  following  recent  publications :  An 
Introduction  to  Theoretical  and  Applied  Colloid  Chemistry  by 
Wolfgang  Ostwald,  translated  by  M.  H.  Fischer,  and  The 
Chemistry  of  Colloids  by  Zsigmondy  and  Spear. 

Ore  Flotation.  —  In  general,  the  process  of  ore  flotation 
consists  in  employing  a  flotation  machine  in  which  are  the 
ore,  which  is  approximately  80  mesh,  and  water  in  the  ratio  of 
3  to  i,  together  with  small  quantities  of  oil.  Air  is  forced 
mechanically  into  this  "  pulp  "  by  means  of  beaters.  Then 
in  this  froth-flotation  process  we  have  the  following  systems 
present :  two  solid-liquid  systems  —  (ore-water)  and  (ore- 
oil)  ;  liquid-liquid  (water-oil)  ;  solid-gas  (ore-air),  and  two 
liquid-gas  systems  —  (water-air)  and  (oil-air) .  These  vari- 
ous phases  have  existing  at  their  respective  surfaces  their 
individual  surface  tensions,  and  these  are  referred  to  as  in- 
terfacial  tension. 

It  is  known  that  the  surface  tension  of  water  is  changed 
by  the  addition  of  various  solutes  or  soluble  contaminants, 
as  they  are  sometimes  called.  All  acids  lower  the  surface 
tension,  and  the  same  is  true  of  oils,  i.e.  the  oil  will  reduce 
the  interfacial  tension  between  the  water-oil  phases.  We 
have  seen  that  this  change  in  surface  tension  is  accompanied 
by  adsorption,  which  results  in  the  increased  concentration  of 
the  contaminating  or  dissolved  substance.  We  also  have  seen 
that  the  surface  film  might  contain  less  of  the  contaminant 
than  the  solution,  when  we  have  negative  adsorption.  That 
is,  we  may  have  a  condensation  of  the  disperse  phase  upon  the 
interfacial  boundary,  while  in  the  case  of  negative  adsorp- 
tion the  disperse  phase  would  be  rejected.  So  in  the  case 
of  two  non-miscible  liquids,  liquid-liquid  system,  we  have  the 
condensation  of  the  disperse  phase  at  the  interface. 

Substances  placed  in  contact  with  water,  and  also  with 
many  other  liquids,  assume  an  electric  charge.  Most  of  these 
substances  in  contact  with  water  become  negatively  charged, 


47°  PHYSICAL  CHEMISTRY 

and  we  have  seen  that  by  the  addition  of  electrolytes  these 
charges  can  be  changed  and  even  reversed.  These  charges 
are  found  in  particles  of  varying  degrees  of  dispersion,  from 
the  ultramicroscopic  particles  to  those  occurring  in  coarse 
suspensions.  Mineral  gangues  such  as  finely  ground  quartz, 
when  suspended  in  water,  are  negatively  charged,  while  sul- 
phide minerals  such  as  pyrite  are  positively  charged.  Oil 
drops  are  negatively  charged,  and  the  same  is  true  of  air 
bubbles,  under  certain  conditions.  In  colloid  systems  these 
contact  films  are  electrically  charged,  and  in  the  case  of  the 
oil-water  contact  film  the  negative  charge  would  tend  to  at- 
tract the  positively  charged  sulphide  particles  of  the  ore, 
causing  this  to  adhere  to  the  interface  of  the  oil-water  sys- 
tem, while  the  gangue  particles  would  be  repelled. 

Upon  the  basis  of  this  electrical  conception  the  flotation  of 
ores  by  means  of  oil  is  considered  to  be  an  electrostatic  pro- 
cess, and  this  electrical  theory  of  Callow  is  stated  as  follows : 
"  It  is  a  scientific  fact  that  when  the  solid  particle  is  suspended 
in  water,  the  water  will  form  around  the  particle  a  contact 
film  which  generally  possesses  an  electric  charge,  the  amount 
and  polarity  depending  upon  the  nature  of  the  surface  of 
the  particle  and  the  electrolyte  in  which  it  is  suspended. 
The  presence  of  these  charges  can  be  demonstrated  by  the 
fact  that  the  particles  possessing  them  will  migrate  when 
placed  in  an  electric  field.  It  has  been  demonstrated  that 
flotable  particles  have  charges  of  one  polarity  (positive), 
and  that  non-notable  particles  have  charges  of  the  opposite 
polarity  (negative) ;  that  the  froth  is  charged  negatively  and 
so  attracts  the  positively  charged  or  flotable  minerals  and 
repels  the  negatively  charged  or  non-flotable  ones.  It  is 
this,  it  is  believed,  that  causes  the  flotable  minerals,  galena, 
sphalerite,  etc.,  to  adhere  to  the  froth,  and  the  gangue  min- 
erals, silica,  etc.,  to  remain  in  the  liquid  where  they  can  be  dis- 
charged as  tailings." 

It  is  maintained  by  some  investigators  that  as  the  electro- 


COLLOID   CHEMISTRY  471 

static  charges  are  small  compared  to  the  size  of  the  particles, 
they  are  hardly  sufficient  to  hold  together  the  particles  of  sul- 
phides and  the  gas.  It  is  therefore  necessary  to  seek  other 
explanations  for  the  flotation  of  minerals  by  the  froth  process. 
They  attribute  the  phenomenon  in  the  froth  process  to  be 
due  to  the  interfacial  surface  tension  which  determines  the 
character  as  well  as  the  formation  of  froths.  A  froth  is  de- 
fined "  as  a  multiplicity  of  bubbles."  As  pure  water  will 
not  produce  a  froth,  it  is  necessary  to  introduce  an  impurity 
which  will  cause  "  a  variable  surface  tension."  The  perma- 
nency of  a  froth  is  greatly  affected  by  the  viscosity,  as  the 
tenacity  of  the  liquid  film  may  be  so  modified  by  securing  the 
proper  viscosity  and  variable  surface  tension  that  the  bubble 
can  be  made  more  or  less  resistant  to  bursting  or  rupture, 
which  is  due  primarily  to  concussion,  pressure,  evaporation, 
and  adhesive  force. 

Anderson  says  :l  "  Solutions  in  which  the  continuous  phase 
is  a  solution  of  soap,  various  products  from  the  saponification 
of  albumens,  etc. ,  will  froth  voluminously  even  in  a  very  dilute 
condition ;  frothing  never  occurring  in  pure  liquids  and  is  a 
definite  proof  that  the  solute  or  disperse  phase  lowers  the  vapor 
tension  of  the  solvent.  A  froth  which  shows  adsorption  at  the 
interfacial  boundary  of  solution  and  gas,  depends  for  its  per- 
sistence on  the  production  of  a  viscous  film  at  that  boundary ; 
these  viscous  films  are  the  direct  result  of  surface  adsorption 
of  the  disperse  phase,  i.e.  dissolved  contaminants,  the  amount 
of  which  is  small  —  disappearingly  so."  The  kind  of  oil  and 
the  amount  of  air  are  important  factors  in  the  production  of  a 
froth  as  well  as  in  insuring  its  stability.  "  The  most  successful 
frothing  oils  include  the  pure  oils,  cresylic  acid  and  turpentines, 
and  other  pyroligneous  products  from  the  distillation  of  wood 
.  .  .  the  coal  tar  phenols  and  their  nearby  derivatives,  and 
almost  all  of  the  so-called  essential  oils  are  good  frothers." 
Pure  oil  makes  a  brittle  froth  which  dies  immediately ;  creosote 
1  MsL  Chem.  Eng.,  15,  82  (1916). 


472  PHYSICAL   CHEMISTRY 

makes  a  stable  elastic  froth ;  coal  tar  products  increase  the  vis- 
cosity but  are  poor  frothing  agents.  An  oil  mixture  of  different 
oils  will  effect  a  better  separation  than  a  single  oil,  as  in  the 
case  of  zinciferous  slimes,  "  the  best  combination  consisted 
of  pure  oil  as  a  frother,  plus  wood  creosote  as  a  froth  and 
selector,  plus  refined  tar  oil  as  a  froth  stiff  ener."  Anderson 
gives  as  the  main  and  essential  requirements  for  froth  flota- 
tion: "  (i)  The  production  of  a  persistent  froth  by  any 
means ;  (2)  the  attachment  of  the  bubbles  of  air  to  the  sul- 
phides or  other  material  to  be  floated ;  and  (3)  the  main- 
taining of  a  selective  action  of  the  froth  bubbles  for  the 
sulphides  or  other  material  to  be  floated." 

Bancroft  says  :  "  We  cannot  get  a  froth  with  a  pure  liquid 
and  air.  There  must  be  present  a  third  substance  in  colloidal 
solution  which  will  tend  to  form  an  emulsion  of  air  in  the 
liquid  in  question,  for  a  froth  is  essentially  a  very  concen- 
trated emulsion  of  air  in  liquid.  If  the  colloidal  material  is 
not  present,  it  must  be  added.  It  has  often  been  overlooked 
that  what  is  needed  for  ore  flotation  is  a  froth  of  air  in  oil. 
The  things  which  have  proved  successful  are  substances  like 
sodium  resinate,  so  called,  which  produce  a  froth  of  air  in 
water  in  an  alkaline  solution  but  one  of  air  in  oil  in  an  acid 
solution,  because  free  rosin  forms  a  colloidal  solution  in  oil 
but  not  in  water ;  .  .  .  substances  which  form  colloidal  solu- 
tions in  oil  and  not  in  water  tend  to  emulsify  water  in  oil." 

The  tendency  of  the  practice  is  to  reduce  the  quantity  of 
oil  used  in  the  process,  and  if  the  amount  is  sufficiently  de- 
creased we  have  the  particle  of  ore  not  surrounded  by  a  film 
of  oil,  but  merely  wetted  partially  with  the  oil,  while  a  part 
of  it  is  in  contact  with  the  water  and  another  part  in  contact 
with  air.  This  gives  then,  in  addition  to  the  effect  of  the  oil, 
the  flotation  effect  of  the  air  as  well.  "  It  is  possible  that  the 
air  film  may  surround  the  oiled  particle  of  ore  completely, 
so  that  the  oil  does  not  come  in  contact  with  the  water.  In 
that  case  we  are  back  to  a  straight  air  flotation  of  oiled  par- 


COLLOID   CHEMISTRY  473 

tides.  This  point  calls  for  further  study  because,  if  es- 
tablished, it  would  have  a  very  important  bearing  on  the 
future  development  of  the  subject.  " 

Preparation  of  Colloid  Systems.  —  According  to  the  classi- 
fication of  colloid  systems  upon  the  basis  of  the  degree  of  dis- 
persion of  the  disperse  phase,  all  methods  for  preparing 
colloid  solutions  can  be  classified  either  as  (i)  condensation 
or  (2)  dispersion  methods. 

The  condensation  methods  diminish  the  dispersivity  to 
within  the  limits  assigned  arbitrarily  to  colloid  systems. 
The  disperse  phase  which  exists  in  the  molecularly  disperse 
condition  may  be  precipitated  by  double  decomposition,  hy- 
drolysis, or  reduction.  In  the  case  of  BaSO4  we  have  a  case 
of  double  decomposition  with  the  formation  of  very  fine 
particles  which  have  a  strong  adsorptive  power.  Aluminium 
hydroxide  is  precipitated,  and  in  the  presence  of  the  ammo- 
nium salts  it  is  converted  into  a  gel ;  but  if  the  ammonium 
salts  are  washed  out,  part  of  the  hydroxide  precipitate  redis- 
solves  with  the  formation  of  the  aluminium  hydroxide  sol. 
This  same  phenomenon  is  marked  in  the  case  of  many  precipi- 
tates, and  the  presence  of  electrolytes  is  necessary  to  prevent 
them  from  forming  colloid  solutions.  Carey  Lea  employed, 
in  the  preparation  of  colloid  solutions  of  silver,  ferrous  citrate 
as  a  reducing  agent.  Zsigmondy  used  formaldehyde  to  pro- 
duce his  gold  sols  from  alkaline  solutions  of  auric  chloride ; 
carbon  monoxide  and  phosphorus  are  also  employed  in  the 
preparation  of  gold  sols,  while  Gutbier  obtained  red  and 
blue  gold  sols  with  hydrazine. 

The  hydrolysis  of  salts  is  a  special  case  of  double  decom- 
position. This  is  a  reversible  reaction  and  increases  with 
the  dilution  as  well  as  with  the  rise  of  the  temperature.  The 
preparation  of  hydrosols  of  the  metallic  hydrates  of  aluminium 
iron,  tin,  bismuth,  cerium,  thorium,  and  zirconium  by  hydroly- 
sis and  the  removal  of  the  free  acid  by  dialysis  are  typical 
examples. 


474  PHYSICAL  CHEMISTRY 

The  dispersion  methods  increase  the  dispersivity  of  the  dis- 
perse phase.  There  are  a  number  of  special  methods  by 
which  this  may  be  accomplished.  Washing  out  precipitat- 
ing reagents  from  finely  divided  precipitates  causes  the  parti- 
cles to  "  run  through  "  the  filter  paper,  thus  demonstrating 
the  necessity  of  the  presence  of  the  electrolyte  to  prevent 
the  precipitate  from  "redissolving,"  that  is,  from  its  dis- 
persivity being  increased.  By  the  addition  of  a  suitable 
peptiser  the  dispersivity  can  be  increased  until  a  sol  is  pro- 
duced, and  a  typical  example  of  this  method  is  peptisation. 
Some  metallic  sulphides  are  peptised  with  hydrogen  sulphide. 
Zinc  hydroxide  and  beryllium  hydroxide  form  sols  when 
treated  with  alkalies.  Sols  of  many  metals,  such  as  chro- 
mium, manganese,  molybdenum,  tungsten,  titanium,  silicon, 
thorium,  platinum,  etc.,  can  be  obtained  by  using  suitable 
peptisers,  which  include  organic  acids,  phenols,  aluminium, 
chloride,  caustic  alkalies,  alkaline  carbonates,  potassium 
cyanide,  and  organic  bases.  The  disperse  means  may  be 
water,  methyl  alcohol,  ethyl  alcohol,  or  glycerine.  By 
mechanical  disintegration  (grinding)  many  substances  can 
be  so  finely  divided  that  they  form  colloid  solutions.  The 
electric  dispersion  method  of  Bredig  (1898)  consists  in  pro- 
ducing by  means  of  a  direct  current  an  electric  arc  between 
electrodes  of  the  metal  to  be  dispersed  under  the  surface  of 
the  liquid  employed  as  the  disperse  means.  Many  hydrosols 
as  well  as  organosols  have  been  prepared  by  this  method. 
Svedberg,  by  using  oscillating  discharges  instead  of  a  direct 
current,  has  prepared  pure  metal  sols  in  water  and  other 
liquids. 


CHAPTER  XXXVI 
RATE   OF  CHEMICAL  REACTIONS 

IN  our  discussion  so  far  we  have  not  considered  that  these 
various  reactions  require  any  time  for  their  performance,  but 
have  rather  assumed  that  the  chemical  reactions  take  place 
instantaneously.  Such  is  not  the  case,  however,  for  all  re- 
actions require  a  definite  period  of  time  for  the  substances 
taking  part  in  the  reaction  to  produce  a  system  that  is  in 
equilibrium.  While  the  transformations  are  themselves  in- 
stantaneous, the  conversion  of  all  of  one  set  of  substances 
into  another  set  depends  upon  many  factors,  one  of  which  is 
the  quantity  of  the  substances  to  be  transformed,  that  is,  the 
mass  of  the  reacting  substances.  In  some  cases  the  whole 
masses  are  transformed  into  new  ones  almost  instantane- 
ously, the  time  of  the  reaction  being  a  small  fraction  of  a 
second,  while  other  reactions  may  require  days  or  even  longer 
periods  for  their  completion.  Connected  with  the  comple- 
tion of  any  reaction  there  are  two  opposing  forces,  one  the 
moving  power  or  the  affinity,  and  the  other  the  resistance  to 
the  reaction  that  comes  into  play.  The  latter  can  be  varied 
considerably,  in  fact  so  much  that  the  speed  of  a  reaction  can 
be  decreased  materially  and  made  so  slow  that  the  reaction 
has  practically  ceased ;  while  the  affinity  is  definite  for  a 
given  state  of  matter.  The  resistance  to  a  reaction  may  be 
caused  by  the  distance  between  the  bodies  reacting,  by  the 
viscosity  of  the  medium  in  which  the  reaction  is  taking 
place,  etc. 

The  reaction  between  zinc  and  sulphuric  acid  may  be 
greatly  decreased  by  subjecting  the  system  to  great  pressure, 

475 


476  PHYSICAL  CHEMISTRY 

where  the  evolution  of  hydrogen  may  cease  entirely.  A 
pressure  of  eighteen  atmospheres  stops  the  reaction,  while 
a  higher  pressure,  when  1.3  normal  sulphuric  acid  is  em- 
ployed, reverses  the  reaction  and  causes  zinc  to  be  precipi- 
tated. Frowein  found  that  the  maximum  vapor  pressure  of 
ZnSO4  •  7  H2O  at  18°  C.  is  8.406  mm.,  and  a  lower  pressure 
produces  a  reversal  of  the  reaction : 

ZnSO4  •  6  H2O  +  H2O  :£  ZnSO4  •  7  H2O. 

In  the  case  of  evaporation  we  have  a  condition  of  equilibrium 
only  when  the  maximum  pressure  of  the  body  vaporizing  is 
equal  to  the  vapor  pressure.  The  rate  of  evaporation  will 
be  proportional  to  the  difference  between  the  two  vapor  pres- 
sures. Noyes  and  Whitney  found  practically  the  same  rela- 
tion for  the  rate  of  solution  of  benzoic  acid  and  of  lead 
chloride,  since  the  rate  of  solution  proved  to  be  proportional 
to  the  difference  between  the  saturated  concentration,  C, 
and  the  concentration  actually  existing,  i.e.  the  rate  of 
solution  is  proportional  to  the  difference  in  concentration 
k(C--c). 

Affinity. — The  idea  of  the  mutual  attraction  of  the  elements 
has  been  emphasized  from  very  early  times,  and  the  prop- 
erty which  causes  the  element  to  enter  into  chemical  com- 
binations is  termed  chemical  affinity.  It  was  Newton  who 
first  considered  that  this  force  was  inherent  in  the  element 
itself,  and  he  showed  that  this  chemical  attraction  decreased 
with  the  distance  more  rapidly  than  the  law  of  gravitational 
attraction  required.  Various  efforts  were  made  to  measure 
the  magnitude  of  this  attraction  and  represent  the  relative 
affinities  of  the  various  substances.  Geoffrey  (1718)  was  the 
first  to  compile  a  table  of  this  character.  The  elements 
were  arranged  in  the  order  of  their  decreasing  attraction,  and 
those  above  would  replace  the  ones  lower  down  from  their 
compounds.  Bergmann  (1775)  found  that  the  conditions  in 
which  a  substance  existed  affected  its  position  in  Geoffrey's 


RATE  OF  CHEMICAL   REACTIONS  477 

table.  These  conditions  were  not  only  the  state  of  aggre- 
gation (solid,  liquid,  or  gas)  of  the  substance,  but  also  the 
temperature  and  the  medium  present  The  value  of  such 
a  table  of  affinities  therefore  became  practically  negligible. 

Wenzel  in  his  discussion  (1777)  of  the  subject  of  affinity 
shows  that  the  conditions  under  which  the  reactions  pro- 
ceded  were  dependent  on  the  masses  of  the  reacting  substances, 
and  he  concluded  that  the  chemical  reaction  is  proportional 
to  the  concentration  of  the  reacting  substances.  Berthollet 
confirmed  this  experimentally  and  in  1801  emphasized  that 
the  masses  of  the  reacting  substances  must  also  be  taken 
into  consideration,  for  the  effect  of  the  mass  may  become 
such  as  to  overcome  completely  the  force  of  affinity.  It 
follows  then  that  the  activity  of  substances  must  be  measured 
by  the  masses  which  produce  a  definite  reaction,  and  this 
Berthollet  stated  as  follows :  "  The  chemical  activity  of  a 
substance  depends  upon  the  force  of  its  affinity  and  upon 
the  mass  which  is  present  in  a  given  volume."  But  this 
idea  of  the  influence  of  the  mass  received  a  great  deal  of  oppo- 
sition and  was  not  accepted.  It  was  not,  however,  until 
almost  two  decades  later  that  Rose  (1842)  emphasized  in  a 
striking  manner  the  action  of  the  mass.  The  decomposi- 
tion of  silicates  in  the  presence  of  water  and  carbon  dioxide 
of  the  air  illustrates  the  breaking  down  of  very  stable  com- 
pounds by  very  weak  chemical  reagents  when  they  are  in 
large  quantities  acting  for  a  long  time.  These  reactions  can- 
not be  duplicated  to  any  appreciable  extent  in  the  laboratory. 
Further,  in  the  crystallization  of  acid  sulphates  of  potassium 
from  boiling  solutions,  a  portion  of  the  sulphuric  acid  is  split 
off  to  combine  with  the  water.  On  redissolving  this  crop  and 
recrystallizing,  the  neutral  salt  is  obtained,  thus  showing  the 
further  splitting  off  of  the  sulphuric  acid  by  the  mass  action 
of  the  water.  Other  investigators  now  took  up  this  work  and 
presented  a  large  number  of  experiments  which  show  the 
marked  effect  of  the  mass  of  the  reacting  substances  on  the 


478  PHYSICAL   CHEMISTRY 

reaction.  In  the  study  of  such  reactions  as  the  decomposi- 
tion of  barium  sulphate  by  boiling  in  a  solution  of  potassium 
carbonate,  it  was  recognized  that  there  are  really  two  re- 
versible reactions  to  be  considered,  and  for  a  particular  con- 
dition, a  maximum  amount  of  decomposition  of  barium 
sulphate. 

It  was  not  until  1850,  when  Wilhelmy  published  his  data  on 
the  inversion  of  cane  sugar,  that  we  had  the  first  method 
outlined  by  which  the  speed  of  the  chemical  reactions  can  be 
measured.  Wilhelmy  showed  that  by  placing  a  sugar  solu- 
tion containing  acid  in  a  polarimeter  tube  and  keeping  the 
temperature  constant,  the  progress  of  the  inversion  of  the 
cane  sugar  could  be  readily  followed  by  observing  the  optical 
condition  at  definite  intervals  of  time.  He  studied  the  re- 
action carefully  at  different  temperatures  with  different 
quantities  of  sugar,  of  acids,  and  with  different  acids,  and 
concluded  that  the  amounts  of  sugar  inverted  in  a  given  time 
were  proportional  to  the  amounts  of  acid  and  of  sugar  present, 
and  this  also  varied  with  the  temperature. 

Several  years  later  (1862)  Berthelot  and  Gilles  studied  the 
formation  of  esters  from  alcohols  and  acids,  and  these  data 
emphasized  the  effect  of  the  mass  on  the  speed  of  these  chemi- 
cal reactions.  They  concluded  that  the  amount  of  ester 
formed  in  unit  time  is  proportional  to  the  product  of  the  con- 
centrations (the  masses)  of  the  reacting  substances  and  in- 
versely porportional  to  the  volume. 

It,  however,  remained  for  Guldberg  and  Waage  (1867) 
to  formulate  mathematically  these  ideas  of  affinity,  the 
effedt  of  mass,  and  the  speed  of  the  chemical  reactions. 
"  We  must  study  the  chemical  reactions  in  which  the  forces 
which  produce  new  compounds  are  held  in  equilibrium  by 
other  forces,"  and  particularly  is  this  true  where  the  reac- 
tions do  not  run  to  an  end  but  are  partial. 

Law  of  Mass  Action.  —  If  by  the  reaction  of  two  sub- 
stances, A  and  B,  the  two  new  compounds,  C  and  D,  are 


RATE  OF  CHEMICAL  REACTIONS  479 

formed,  the  chemical  equilibrium  would  be  represented  thus, 
A  +  B  ^±  C  -f-  D.  The  substances  A  and  B  combine  to 
produce  C  and  D,  while  under  the  same  conditions  C  and 
D  react  to  produce  A  and  B,  and  when  equilibrium  is  es- 
tablished the  four  substances  are  present.  There  is,  then, 
a  force  causing  the  union  of  A  and  B  with  the  formation  of 
C  and  D,  thus  resulting  in  the  reaction  going  from  left  to 
right  at  a  certain  velocity.  This  velocity  was  shown  by 
Guldberg  and  Waage  to  be  proportional  to  the  product  of 
the  active  masses  of  the  two  substances,  that  is,  the  velocity 
=  k  •  a  •  b,  in  which  a  and  b  are  the  active  masses  of  A  and 
B  respectively,  and  k  is  the  affinity  coefficient.  Similarly, 
in  the  reverse  reaction  in  the  re-formation  of  the  substances 
A  and  B  by  the  reaction  of  C  and  D,  we  have  a  velocity 
which  is  equal  to  k'  •  c  •  d,  in  which  c  and  d  are  the  active 
masses  of  C  and  D  respectively,  and  k'  is  the  affinity  coeffi- 
cient. As  this  is  an  equilibrium  equation,  it  represents  the 
reaction  from  right  to  left  proceeding  at  the  same  rate 
as  the  reaction  from  left  to  right,  and  in  unit  time  there  are 
as  many  moles  of  A  and  B  decomposed  to  form  C  and  D 
as  there  are  of  C  and  D  decomposed  to  re-form  A  and  B. 
That  is,  the  velocities  of  these  two  reactions  are  equal,  and 
we  then  have  k  •  a  •  b  =  k'  •  c  •  d. 

If  the  reaction  is  in  a  state  of  equilibrium  as  just  illus- 
trated, then  the  velocity  of  the  reaction  represented  by  the 
reaction  of  the  substances  A  and  B  must  be  equal  to  the 
velocity  of  the  reaction  of  C  and  D,  i.e.  v  =  v'  and  v  = 
k  -  a  •  b  and  v'  =  k'  •  c  -  d.  But  where  the  velocity  in  one 
direction  is  different  from  that  in  the  opposite  direction, 
the  reaction  is  going  to  proceed  more  rapidly  in  that  direc- 
tion, and  as  a  result  the  reaction  as  a  whole  proceeds  in  that 
direction.  We  speak  of  the  reaction  running  to  an  end,  i.e. 
until  there  is  a  complete  predominance  of  one  of  the  two 
systems.  The  velocity  of  the  reaction  V  is  defined  as  the 
difference  between  the  individual  velocities,  i.e.  V  =  v  —  v', 


480  PHYSICAL   CHEMISTRY 

or  V  =  k  •  a  •  b  —  k'  •  c  -  d,  which  is  the  fundamental  ex- 
pression for  the  velocity  of  reactions.  In  the  expression 

k  •  a  •  b  =  k'  •  c  •  d  or  —  =  —     -   we  recognize  the  Mass  Law 
k       a  •  b 

Equation,  and  the  equilibrium  constant  —  =  K.     The  Guld- 

*•  K 

berg-Waage  expression  for  the  velocity  of  the  reaction  when 
the  velocities  of  the  two  systems  are  equal  is  identical  with 
the  above  expression,  showing  the  reaction  to  be  propor- 
tional to  the  products  of  the  reacting  masses. 

Thermodynamic  Deduction  of  the  Law  of  Mass  Action.  —  Lewis  by 
means  of  an  isothermal  reversible  cycle  in  which  the  "Equilibrium  Box" 
of  van't  Hoff  is  employed  gives  the  following  thermodynamic  deduc- 
tion of  the  Mass  Law  Equation  for  a  homogeneous  gaseous  system.  In 
the  reaction  A  +  B  ^  C  +  D  let  the  four  gaseous  substances  be  in  the 
two  reservoirs,  I,  II,  with  the  concentrations 
a,  b,  c,  d,  and  a',  b',  cf,  d',  respectively.  The 
temperature  of  the  two  reservoirs  is  the 
same,  and  the  substances  are  in  equilibrium. 
I.  Iso  thermally  and  reversibly  remove  one 
•pIG  g  "  mole  of  A  from  I  at  its  partial  pressure  pA, 

and  the  volume  will  be  VA.     The  work  done 

by  the  system  is  -J-  pA  VA.  Now  change  pA  to  pA  reversibly,  and  simul- 
taneously the  volume  changes  from  VA  to  VA.  The  work  done  is  then 

V 


CA 

Jy 
into  II,  the  work  is  —  pA  VA.     Then  the  summation  of  the  work  done  is 


y      pdV.    Now  force  the  mass  of  gas,  one  molecular  volume  VA  ', 


Assume  The  Gas  Law,  pV  =  nRT;  since  T  is  constant,  then  pV  =  a 
constant.     As  we  have  the  same  mass  of  gas  it  follows  that  pAVA  = 

CV   ' 

pA'VA,  hence  the  total  work  done  is    )„     pdV,  which  in  this  case  is 

JV  A 

equal  to  }pA,Vdp. 

II.   Similarly  and  simultaneously  with  the  transfer  of  A  let  one  mole 
of  B  be  transferred  from  I  to  II.     Then 


RATE  OF  CHEMICAL  REACTIONS  481 

the  work  per  mole  of  B  =  J    Bt  VB  dp. 

As  the  system  is  gaseous,  assuming  The  Gas  Law  to  hold,  we  have 

pA  =  RTa  and  pA'  =  RTa' 
hence  the  work  on  A  =  RT  log  — 

and  the  work  on  B  =  RT  log  —  . 

III.  Now  in  equilibrium  box  II,  assume  that  the  moles  of  A  and  B 
added  are  changed  into  C  and  D  and  no  external  work  is  done. 

IV.  Finally  transfer  one  mole  of  C  and  one  mole  of  D  from  II  to  I  in 
the  above  manner.     Then 

work  =  RT  log  c-  +  RT  log  ^- 
c  a 

Now  let  these  molecules  of  C  and  D  change  into  A  and  B  in  I  and  as- 
sume no  external  work  is  done.  The  initial  conditions  have  been 
restored  and  the  cycle  is  complete.  Since  this  was  accomplished  iso- 
thermally  and  reversibly  the  summation  of  the  work  done  is  zero. 
Hence  we  have 

*riog  ±  +  RT  log  £  +  RTlog  c-  +  RTlog  3   =  o  or 
abed 

log  a  +  log  b  —  log  c  —  log  d  =  log  a'  +  log  b'  —  log  c'  —  log  d' 
which  becomes 


=  a  constant. 


c  '  d     c    '  d 

This  is  the  Law  of  Mass  Action  for  a  system  following  The  Gas  Law 
and  is  Guldberg-Waage's  expression. 

We  have  seen  that  when  two  substances  A  and  B  react 
to  form  C  and  D  the  velocity  of  the  action  of  A  on  B  is 
v  —  k  -  a  •  b;  but  it  is  apparent  that  this  velocity  must 
change  as  the  reaction  proceeds,  since  the  concentrations  of 
A  and  B,  a  and  b  respectively,  are  changing  continuously. 
Let  us  assume  that  x  moles  of  A  and  of  B  have  been  used 
up  in  the  definite  time  /,  then  the  concentrations  of  A  and  B 
at  the  end  of  this  time  will  be  (a  —  x)  and  (b  —  x)  respectively, 
and  we  have  for  the  reaction  velocity 

v  (after  time  /)  =  k(a  —  x)(b  —  x). 


•    __- 
482  PHYSICAL  CHEMISTRY 

During  this  time  /  the  concentrations  of  C  and  of  D  will  like- 
wise have  increased  to  (c  +  x)  and  (d  +  x)  respectively,  and 
v'  (after  time  /)  =k'(c  +  x)(d  +  x).  We  then  state  that  the 
small  amount  of  A  changed,  dx,  in  the  small  interval  of 
time,  dt,  would  be 

<^  =  k(a-  x)(b  -x)  -  k'(c  +  x)(d  +  x). 
dt 

But  if  the  reaction  of  the  resulting  products  of  the  reaction 
is  so  slight,  that  the  speed  of  the  reverse  reaction  can  be 
neglected  entirely,  then  the  reaction  velocity  equation 
becomes 


Or  if  there  is  only  one  substance,  A ,  undergoing  decomposi- 
tion into  products  which  do  not  react,  then  the  equation  takes 

the  form  -^  =  k(a  —  x),  which  is  Wilhelmy's  law  that  the 
dt 

velocity  of  the  chemical  reaction  at  any  moment  will  be  pro- 
portional to  the  amount  of  the  substance,  a,  actually  pres- 
ent. Or,  as  Harcourt  and  Esson  state  it,  "  the  amount  of 
chemical  change  in  a  given  time  is  directly  proportional  to 
the  quantity  of  reacting  substance  present  in  the  system." 
Equation  for  Monomolecular  Reactions.  —  The  differen- 

dx 

tial  equation  ^7  =  k(a  —  x)  is  then  a  mathematical  expres- 
sion of  the  theory  of  the  speed  of  reaction.  Reactions  which 
correspond  to  an  equation  of  this  type  are  termed  mono- 
molecular.  The  equation  contains  the  variables  -j.  and  x 

and  the  constants  k  and  a.  If  different  sets  of  corresponding 
values  of  these  variables  be  determined  experimentally,  to- 
gether with  the  value  of  a,  and  substituted  in  the  equation, 
the  computed  values  for  k  should  agree.  It  is  of  course  im- 


RATE  OF   CHEMICAL  REACTIONS  483 


possible  to  get  instantaneous  values  of  -^,  and  the  approxima- 

te 

tions  that  can  be  obtained  do  not  give  satisfactory  results. 
It  is  therefore  necessary  to  obtain  another  equation,  the 
terms  in  which  can  be  readily  and  accurately  measured.  It 
is  possible  to  derive  another  equation  involving  the  same 
constant,  k,  by  integrating  this  differential  equation. 

The  equation  -^  =  k(a  —  00}  may  be  written 
at 

dx 

=  kdt,  which  on  integration  gives 


which  becomes 

—  loge  (a  —  x)  —  kt  =  C. 

At  the  initial  conditions  /  =  o  and  oc  =  o,  the  equation 
becomes 

C  =  -  log,  (a  -  o)  -  fco  =  -  log.  a. 

Substituting  this  value  for  C  in  the  above  equation  and 
solving  we  have 

kt  =  log,  a  —  log,  (a  —  x)  or 

kt  =  log,  —  -  —  or 
a  —  x 


t         a  -  * 

It  is  customary  to  use  the  logarithms  to  the  base  10,  log, 
instead  of  the  natural  logarithms,  loge;  then  the  equation 
becomes 

0.4343  k  =  -  log  — - — 
t         a  —  x 

It  is  evident  that  since  this  is  a  constant  it  could  be  ex- 
pressed directly  in  terms  of  log,  and  the  equation  takes  the 
form 

/          a  —  x 


484  PHYSICAL   CHEMISTRY 

which  may  be  considered  a  special  case  of  the  general 
formula. 

Equation  for  Bimolecular  Reactions.  —  Reactions  wherein 
there  are  two  of  the  reacting  substances  changing  in  concen- 
tration during  the  reaction  are  termed  bimolecular  reactions. 
The  reaction  velocity  at  any  moment  is  given  by  the  differ- 
ential equation  -^  =  k(a  —  x)(b  —  x),  in  which  a  and  b 
at 

represent  the  concentrations  of  the  two  substances  the  con- 
centrations of  which  are  changing.  Let  x  represent  the 
amount  of  one  substance  that  has  changed  in  time  /,  then  the 
same  number  of  moles  of  the  second  substance  will  have 
changed  during  the  same  time.  If  we  assume  that  there  are 
the  same  number  of  moles  of  the  two  substances  present  at 
the  beginning  of  the  reaction,  then  a  =  b  and  the  equation 

becomes  -^  =  k(a  —  x)2 ;      or    rearranging,   dt  =        x 


dt  k(a—x)2- 

Integrating,  we  obtain  /  =  — — -f  constant.     Evaluating 

k(a  -  x) 

the  constant  in  the  usual  way  by  putting  x  =  o  and  /  =  o  and 
substituting,  we  hz 
stituting,  we  have 


substituting,  we  have  the  integration  constant  =  —  -^-.     SUD- 

ka 


k(a  -x)     ka 
and  simplifying 


or  k  =  - 


ka(a  —  x)  t  a(a  —  x) 

If,  however,  the  quantities  of  A  and  B  are  not  equal,  then 
the  equation  is 

^  =  k(a-x)(b-x) 

which  may  be  rewritten 

'     -<**-(     *      -      *     \=  kdt. 
a  —  b\b  —  x     a  —  xj 


RATE   OF   CHEMICAL   REACTIONS  485 

Integrating,  we  obtain 

--  —  -  (log  -  )  =  kt  +  constant. 
a  —  b\    *  a  —  xj 

If  x  =  o  and  t  =  o,  substituting,  we  have 


1      log  -  =  a  constant. 


a  -  b     °  a 
Introducing  this  value,  the  equation  becomes 

l—  (log^-?-}  =kt-  -^-r  log  -  • 

a  —  b\      a  —  xj  a  —  b       a 

Solving, 

b  —  x 

7        ~~t3  1 O 

^a  —  b         a     a  —  o         a  —  x 
which  simplifies  to 

<-^^|5f-        - 

Equation  for  Trimolecular  Reactions.  —  If  there  are 
three  reacting  substances  and  x  represents  the  number  of 
moles  of  each  entering  into  the  reaction  in  the  time  t,  then 

dx  * 

—  =  k(a  —  x)(b  —  x)(c  —  x).     The  simplest  case  is  where 
at 

the  three  reacting  substances  are  in  equivalent  proportions. 

Then  the  equation  takes  the  form  -~-=  k(a  —  x)3,  which  on 

at 

integration  and  by  the  evaluation  of  the  integration  constant 
gives 

T   _  i  x(2  a  —  x) 
—  ~     — / —  — \~~  * 

Degree  of  the  Reaction.  —  The  number  of  different  molec- 
ular species  whose  concentration  changes  during  the  course 
of  the  reaction  is  used  as  the  basis  for  designating  the  order 
of  the  reaction.  The  reactions  are  termed  monomolecular 
when  only  one  molecular  species  changes  in  concentration ; 
bimolecular,  when  two  change ;  trimolecular,  when  three 


486  PHYSICAL   CHEMISTRY 

constituents  change  in  concentration,  etc.  The  three  equa- 
tions just  derived  are  very  different,  and  the  question  arises, 
how  can  they  be  used  to  determine  the  order  of  a  chemical 
reaction?  By  substituting  in  the  equations  the  different 
times,  /,  at  which  the  concentrations,  x,  are  determined,  and 
knowing  the  initial  concentration,  the  velocity  constant 
can  be  calculated.  The  formula  which  gives  a  constant  value 
would  designate  the  order  of  the  reaction.  It  is,  however, 
necessary  to  make  but  a  few  determinations,  for  if  the  time 
in  which  one  half  of  the  material  available  for  transformation 
is  known,  the  relation  between  the  time  and  the  original  con- 
centration of  the  constituent  is  very  characteristic  for  the 

different  types  of  reactions.     If  %  =  - ,  on  substituting  this 

2 

value  in  the  equation  for  monomolecular  reactions  and  solv- 
ing for  /,  we  find  that  the  time  is  independent  of  the  original 
concentration,  i.e.  substituting,  we  have 

tk  =  log  2. 

As  the  original  concentration  does  not  appear  in  the  equa- 
tion, the  time  /  is  independent  of  the  original  concentration. 
This  is  known  as  the  period  of  half  change.  Similarly,  it 
may  be  shown  that  for  bimolecular  reactions  the  time  is 
inversely  proportional  to  the  initial  concentration,  and  for 
trimolecular  reactions  it  is  inversely  proportional  to  the 
square  of  the  initial  concentration.  In  general,  the  time 
required  to  change  one  half  o'f  the  substance  present  under- 
going the  chemical  change  is  inversely  proportional  to  the 
(n  —  i)th  power  of  the  initial  concentration.  The  order  of 
the  reaction  is  then  readily  established. 

Reactions  of  different  degrees  of  complexity  are  known, 
and  those  to  the  eighth  order  have  been  described.  When 
the  number  of  reacting  substances  is  increased,  reactions 
between  the  original  constituents  and  the  new  constituents 
become  possible  as  well  as  the  reactions  between  the  new 


RATE  OF  CHEMICAL  REACTIONS  487 

constituents  themselves.  There  will  result  a  number  of  side 
reactions  which  will  be  of  different  orders,  depending  on  the 
number  of  molecular  species  produced  by  the  original  re- 
action as  well  as  by  the  secondary  side  reactions.  Then 
there  will  be  reactions  which  are  opposite  to  the  original 
reactions.  These  may  take  place  at  the  same  time  as  the 
original  reaction,  or  they  may  be  at  a  different  time,  thus 
giving  rise  to  what  is  termed  consecutive  reactions.  So  the 
actual  rate  of  a  reaction,  which  is  what  we  understand  by 
the  velocity  constant,  will  be  dependent  upon  the  relative 
rates  of  the  other  reactions,  and  the  value  will  be  the  sum 
of  all  the  intermediate  independent  changes.  Our  discussion 
will  be  confined  to  a  few  examples  of  the  simple  cases  free 
from  these  auxiliary  reactions. 

Monomolecular  Reactions  Running  One  Way.  —  Reac- 
tions of  the  first  order  are  very  common,  and  among  these  may 
be  mentioned  reduction  of  potassium  permanganate ;  reduc- 
tion of  hydrogen  peroxide ;  decomposition  of  diazo  com- 
pounds ;  decomposition  of  chlor-  and  brom-acetates  ;  forma- 
tion of  anilids  ;  formation  of  esters  in  methyl  alcohol ;  cataly- 
sis of  sulphonic  esters  ;  the  conversion  of  persulphuric  acid  into 
"  Caro's  "  acid  ;  decomposition  of  nickel  carbonyl ;  hydroly- 
sis of  starch ;  hydrolytic  action  of  yeast,  and  inversion  of 
sugar. 

The  inversion  of  cane  sugar  by  acids  and  salts  in  aqueous 
solutions  is  one  of  the  important  chemical  reactions  that 
fulfill  the  conditions  for  a  reaction  of  the  first  order,  since 
it  has  been  found  that  the  concentration  of  the  hydrolyzing 
or  inverting  agents  remains  constant  throughout  the  reac- 
tion. The  equation  representing  the  reaction  is 

C12H22Oii  +  H2O  ^  C6H12O6  +  C6H12O6. 

dextrose  levulose 

This  appears  to  be  a  bimolecular  reaction,  but  the  amount 
of  the  water  that  enters  into  the  reaction  is  so  small  com- 
pared with  the  amount  of  solvent  present  that  its  concentra- 


488  PHYSICAL  CHEMISTRY 

tion  remains  practically  constant.  This  reaction  may  be 
carried  out  experimentally  by  placing  equal  volumes  of  a  20 
per  cent  sugar  solution  and  a  fourth  normal  acid  solution  into 
a  number  of  small  flasks  which  have  been  freed  from  alkali 
by  thorough  steaming.  These  flasks  are  placed  in  a  water 
bath,  which  is  maintained  at  a  constant  temperature.  At 
convenient  intervals  of  time  (about  30  minutes)  one  flask 
is  removed  and  the  sugar  determined  by  the  polarimeter. 
Having  determined  the  initial  concentration  (polarimeter 
reading)  at  the  time  of  mixing  the  acid  and  sugar  solutions 
and  the  readings  for  several  hours,  the  solution  is  permitted 
to  stand  for  several  days  or  is  heated  to  obtain  the  end  point 
of  the  reaction,  that  is,  the  point  of  complete  inversion.  The 
value  obtained  in  this  manner  does  not  always  agree  with 
the  value  calculated  from  the  weight  of  sugar  employed.  A 
number  of  experimenters  have  shown  that  the  specific  rota- 
tion is  dependent  on  the  concentration,  time,  temperature, 
and  also  upon  the  acid  used.  By  substituting  the  data  in 

the  equation  k  =  -  log  — - —  and  solving  for  k,  the  values 
/          a  —  x 

for  the  velocity  constant  or  coefficient  may  be  obtained  as  illus- 
trated in  Table  LXXXVIII.  It  is  immaterial  in  what  units 
the  concentration  a,  of  the  substance  changing  is  expressed. 
So  it  is  usually  convenient  to  employ  the  values  as  expressed 
by  the  scale  of  the  polarimeter  for  designating  the  values  of 
a  and  of  x.  In  Table  LXXXVIII  /  represents  the  time  in 
minutes,  after  the  solutions  of  sugar  and  acid  were  mixed,  when 
the  polarimeter  reading  was  taken ;  a  the  reading  on  the 
scale ;  x  the  difference  between  the  initial  reading  and  the 
reading  at  the  given  time.  In  the  last  column  are  given  the 
values  for  k,  which  indicate  a  good  constant  value. 

From  an  inspection  of  the  equation  it  will  be  seen  that 
there  are  no  factors  that  take  into  account  the  concentration 
of  the  sugar  or  of  the  hydrolyzing  agent.  Ostwald  from  his 
experimental  results  showed  that  the  concentration  did  have 


RATE   OF   CHEMICAL  REACTIONS 


489 


an  effect  on  the  velocity  coefficient.  Cohen,  however,  con- 
sidered that  the  molecules  in  a  concentrated  sugar  solution 
have  a  shorter  free  path  of  motion  than  those  in  less  concen- 
trated solutions,  and  since  the  speed  is  proportional  to  the 
free  path  it  is  proportional  to  the  actual  space  occupied  by 
the  sugar  molecules.  By  applying  the  proper  correction  for 
this,  he  concluded  that  the  concentration  did  not  affect  the 
velocity  constant,  i.e.  it  is  independent  of  the  concentration 
of  the  sugar. 

TABLE  LXXXVIII  —  INVERSION  OF  CANE  SUGAR 
a  (total  change)  =  65.50 


/ 

a  READING 

* 

k 

o 

46.750 



30 

41.00 

5-75 

0.001330 

60 

35-75 

II.OO 

1332 

90 

30.-75 

16.00 

1352 

1  20 

26.00 

20.75 

1379 

150 

22.00 

24-75 

1321 

2IO 

15.00 

31-75 

1371 

330 

2-75 

44.00 

1465 

510 

-    7.00 

5375 

1463 

630 

—   IO.OO 

56.75 

1386 

io-75 

CL   —  65.50 

Inversion  of  Cane  Sugar  by  Acids.  —  It  is  only  in  the  pres- 
ence of  acids  that  the  inversion  of  sugar  proceeds  at  a  marked 
velocity.  The  concentration  of  the  acid  does  not  change 
during  the  reaction.  The  action  of  the  acid  is  said  to  be 
catalytic.  The  greater  the  concentration  of  the  acid  the 
greater  the  velocity  of  inversion  of  the  sugar.  The  nature  of 
the  acid  has  a  marked  effect  on  the  velocity  of  the  inversion. 
The  so-called  strong  mineral  acids  cause  the  inversion  to  pro- 
ceed rapidly,  while  under  the  effect  of  weak  organic  acids  the 
action  is  much  less  pronounced.  It  will  be  recalled  that  the 
definition  of  an  acid  is  that  it  is  a  substance  in  aqueous  solu- 


4QO  PHYSICAL  CHEMISTRY 

tions  that  yield  hydrogen  ions.  The  strength  of  an  acid  is 
attributed  to  the  hydrogen  ions  present  due  to  the  dissocia- 
tion of  the  acid,  that  is,  the  greater  the  degree  of  dissociation 
the  greater  the  hydrogen  ion  concentration.  In  the  case  of 
the  inversion  the  greater  the  concentration  of  the  hydrogen 
ions  the  quicker  the  inversion  of  the  cane  sugar.  Trevor 
(1892)  used  the  inversion  of  cane  sugar  as  a  means  of  deter- 
mining the  concentration  of  the  hydrogen  ions,  i.e.  of  the 
degree  of  dissociation  of  the  acids.  This  method  has  been 
employed  extensively  for  establishing  the  relative  strength  of 
acids  and  in  Table  LVIII,  page  356,  is  given  in  one  column  the 
relative  values  referred  to  hydrochloric  acid  taken  as  i.ooo. 
These  values  give  an  excellent  idea  of  the  variability  of  the 
inversion  coefficients  of  the  various  acids. 

It  will  be  remembered  that  certain  organic  salts  undergo 
hydrolytic  dissociation  with  the  formation  of  hydrogen  ions. 
Trevor  employed  the  inversion  of  cane  sugar  as  a  method  for 
the  determination  of  the  degree  of  dissociation  of  a  number 
of  the  sodium  salts  of  organic  acids,  and  W.  A.  Smith  also 
determined  the  hydrolytic  dissociation  of  organic  salts  by 
this  method  and  compared  the  values  with  those  obtained 
by  the  electrical  conductivity  method.  Long  published  the 
results  of  his  experiments  on  the  inversion  of  .cane  sugar  by 
inorganic  salts.  His  results,  given  in  Table  LXXXIX,  will 
illustrate  the  type  of  reactions  and  the  constancy  of  the 
value,  k,  obtained  for  the  velocity  constant. 

The  data  show  that  in  the  solutions  employed  the  normal 
solution  inverted  the  sugar  but  little  more  rapidly  than  the 
half  normal  solution.  From  the  data  obtained  he  calculated 
the  degree  of  hydrolytic  dissociation  of  these  salts. 

The  addition  of  normal  binary  salts  with  a  common  ion 
to  an  acid  has  a  marked  effect  upon  the  velocity  of  inversion 
of  cane  sugar.  For  example,  potassium  chloride  added  to 
a  solution  of  cane  sugar  containing  hydrochloric  acid  greatly 
increases  the  velocity  of  inversion,  while  the  addition  of  a 


RATE   OF   CHEMICAL   REACTIONS 


49 1 


salt  to  a  weak  organic  acid  with  a  common  ion  greatly  de- 
creases the  velocity.  Arrhenius  says,  "  The  catalytic  activity 
of  hydrogen  ions  is  greatly  stimulated  by  the  presence  of 
other  ions." 

TABLE  LXXXIX  —  INVERSION  OF  CANE  SUGAR  BY 
FeSO4  •  7  H2O 


0.5  NORMAL 

NORMAL 

0=17.12 

0=17.10 

/ 

a 

X 

k 

/ 

a 

X 

i 

0 

12.97 

0 

12.95 

15 

12.48 

0.49 

0.00084 

15 

12.45 

0.50 

0.00086 

45 

11.50 

1.47 

0.00086 

45 

11.26 

1.69 

O.OOIOO 

75 

10.40 

2.57 

0.00094 

75 

10.08 

2.87 

0.00106 

135 

8-43 

4-54 

0.00099 

135 

8.07 

4.88 

0.00108 

195 

6.72 

6.25 

O.OOIOI 

195 

6.30 

6.65 

O.OOIIO 

255 

5.21 

7.76 

O.OOI02 

255 

4.70 

8.25 

O.OOII2 

375 

2.87 

10.10 

0.00103 

375 

2.25 

10.70 

0.00114 

495 

1.03 

11.94 

0.00105 

495 

0.15 

12.80 

O.OOI2I 

Average 

0.00099 

Average 

O.OOI07 

The  inversion  of  cane  sugar  can  then  be  utilized  in  the 
determination  of  the  degree  of  electrolytic  dissociation  as 
well  as  of  hydrolytic  dissociation. 

Bimolecular  Reactions  Running  One  Way.  —  Chemical 
reactions  in  which  two  molecular  species  are  simultaneously 
undergoing  change  are  common.  A  few  of  the  different 
bimolecular  reactions  may  be  mentioned :  the  esterfication 
of  the  chloracetic  acids  ;  bases  and  esters  in  aqueous  as  well 
as  in  alcoholic  solutions  ;  formation  of  methyl  orange ;  am- 
monium cyanate  into  urea ;  oxidation  of  formaldehydes  ; 
hydrolysis  of  amids;  the  action  of  bromine  on  the  fatty 
acids  ;  formation  of  esters. 

One  of  the  best-known  examples  of  a  reaction  of  the  second 
order  is  the  saponification  of  esters.  By  mixing  a  base  and  an 
ester  in  aqueous  solution  there  are  gradually  formed  an  alcohol 


49  2  PHYSICAL   CHEMISTRY 

and  a  salt  of  the  corresponding  organic  acid.     This  may 
be  illustrated  by  the  following  chemical  equation  : 


NaOH^±C2H5OH  +  CH3COONa 

ethyl  sodium  ethyl  sodium 

acetate  hydroxide  alcohol  acetate 

In  order  to  determine  the  velocity  of  this  reaction  equal 
volumes  of  ester  and  the  base  of  the  same  molecular  concen- 
tration are  mixed  in  a  flask  and  placed  in  a  constant  tempera- 
ture bath.  At  convenient  intervals  of  time,  /,  a  definite  quan- 
tity of  this  mixture  is  pipetted  into  a  definite  excess  quantity 
of  standard  acid.  The  excess  is  determined  by  titration,  and 
the  alkali  at  this  time  can  be  calculated  ;  and  if  the  original 
concentration,  a,  is  known,  the  velocity  can  be  calculated  by 
means  of  the  bimolecular  reaction  equation 


/  a  (a  -  x) ' 

since  the  two  substances  changing  simultaneously  were  taken 
in  equal  molecular  quantities. 

This  equation  contains  no  term  designating  the  nature  of 
the  ester  or  of  the  saponifying  agent,  and  the  question  has 
been  raised  whether  they  do  affect  the  velocity  of  saponifica- 
tion  and  also  whether  an  excess  of  either  would  have  any  in- 
fluence. Reicher  attempted  to  answer  this  and  obtained 
data  which  show  that  different  bases  give  different  values 
for  the  constant.  This  is  illustrated  by  the  following  data 
for  methyl  acetate,  using  bases  of  the  same  concentration  : 


BASE 

CONSTANT 

NaOH      

2.307 

KOH         

2.298 

Ba(OH)2        .     . 

2.144 

Ca(OH)2        

2.285 

Sr(OH)2         .     .     . 

2.204 

NH4OH         

O.OII 

RATE  OF   CHEMICAL  REACTIONS 


493 


The  strong  bases  all  give  practically  the  same  value  for  the 
constant  coefficient,  while  the  saponification  by  ammonium 
hydroxide  takes  a  much  longer  time. 

That  the  alcohol  radical  has  a  marked  influence  is  shown 
from  the  following  data,  which  give  the  constant  for  the 
saponification  of  these  various  acetates  by  solutions  of  sodium 
hydroxide  of  the  same  concentration : 


ESTER 

CONSTANT 

Methyl  acetate                                        «     . 

34Q-J 

Ethyl  acetate       »• 

2  TtO7 

Propyl  acetate 

I  Q2O 

Isobutyl  acetate       
Isoamyl  acetate        .' 

1.618 
1.645 

The  more  complex  the  radical  the  less  the  speed  of  saponi- 
fication, and  that  the  same  is  true  for  the  acid  radicals  is 
shown  from  the  following,  which  illustrate  the  saponification 
of  the  esters  by  sodium  hydroxide : 


ESTER 

CONSTANT 

Ethyl  acetate       

-i  204. 

Ethyl  propionate      
Ethyl  buty  rate    .     .     .     .  '  '.     .     .     .     . 
Ethyl  isobutyrate       ;   *;    
Ethyl  isovalerate           
Ethyl  benzoate         

2.816 
1.702 
1.831 
0.614 
0.830 

The  work  of  Reicher  has  been  confirmed  by  Bugarsky  and 
others,  including  Ostwald,  who  further  emphasize  the  fact 
that  the  speed  of  saponification  of  esters  is  a  function  of  the 
concentration  of  the  hydroxyl  ions  and  is  therefore  dependent 
on  the  degree  of  dissociation  of  the  base.  Conversely,  the 
saponification  of  esters  may  be  employed  as  a  method  for  the 


494  PHYSICAL  CHEMISTRY 

determination  of  the  degree  of  electrolytic  dissociation,  that 
is,  the  concentration  of  the  hydroxyl  ions.  The  rate  of 
saponification  can  be  followed  by  the  conductivity  method, 
and  the  values  of  the  velocity  constant  as  found  by  different 
investigators  agree  well. 

Saponification  of  esters  by  weak  bases,  such  as  ammonium 
hydroxide,  methylamine,  ethylamine,  etc.,  proceeds  slowly 
and  gives  a  small  velocity  constant  which  varies  with  the 
time.  Ammonium  hydroxide  gives,  for  example,  the  values 
1.76  :  i. 21 :  i. 01  :  0.845  :  0.501.  Ostwald  showed  that  neutral 
salts  have  a  marked  effect  upon  the  rate  of  saponification 
by  weak  bases  particularly,  and  attributed  their  variations 
to  this  cause. 

It  has  also  been  shown  that  saponification  can  be  produced 
by  substances  that  on  hydrolysis  yield  alkaline  solutions,  and 
since  the  rate  is  proportional  to  the  concentration  of  the 
hydrogen  ions,  this  method  may  be  employed  as  a  means 
of  determining  the  degree  of  hydrolytic  dissociation.  See 
Table  LXVI,  page  393. 

Other  Molecular  Reactions.  —  There  are  numerous  reac- 
tions of  a  higher  order  than  those  in  which  only  two  molec- 
ular species  take  part.  In  many  of  these  there  are  secondary 
reactions  which  are  not  only  reverse  reactions  which  prevent 
the  major  reaction  from  going  to  completion,  but  also  side 
reactions  which  result  from  the  inter-reactions  with  the 
products  of  the  reaction.  These  side  reactions  may  be 
simultaneous  with  the  main  reaction  or  they  may  be  consec- 
utive. When  a  number  of  substances  are  present,  they  may 
react  so  that  there  is  a  series  of  consecutive  reactions.  The 
most  pronounced  example  of  consecutive  reactions  probably 
is  the  formation  of  radium  emanations.  This  is  true  not 
only  in  the  case  of  homogeneous  reactions  but  we  may  also 
have  reactions  of  different  orders  in  the  case  of  heterogene- 
ous chemical  changes  wherein  the  reacting  substances  are 
in  different  states  of  aggregation.  For  a  discussion  of  these 


RATE  OF  CHEMICAL  REACTIONS  495 

the  student  is  referred  to  special  texts  on  advanced  Physical 
Chemistry. 

Factors  which  Influence  the  Velocity  of  Reactions.  —  Iron 
exposed  to  air  combines  slowly  with  the  oxygen  at  ordinary 
temperature.  If  a  piece  of  iron  picture  wire  is  heated  and 
introduced  into  oxygen,  the  iron  burns  very  rapidly  with  an 
evolution  of  much  heat  and  light.  The  reaction  is  of  such 
velocity  at  this  higher  temperature  that  the  heat  developed 
is  greater  than  can  be  conducted  or  radiated  away,  so  that 
the  heat  in  turn  accelerates  the  reaction.  Similarly,  for  many 
other  substances  there  is  no  reaction  between  them,  or  the 
reaction  proceeds  slowly  at  the  lower  temperatures.  On  in- 
creasing the  temperature  the  speed  of  the  reaction  increases 
until  a  temperature  is  reached  at  which  the  heat  generated 
exceeds  that  conducted  or  radiated  away,  and  the  mass  be- 
comes incandescent,  breaks  into  a  flame,  or  ignites.  With 
liquids  such  as  oils  we  designate  this  the  flash  point,  with 
gases  it  is  the  temperature  of  explosion.  This  minimum 
temperature  at  which  combustion  or  explosion  takes  place 
is  designated  the  ignition  temperature,  or  the  kindling  tem- 
perature. 

When  phosphorus  is  placed  in  air,  the  reaction  with  the 
oxygen  is  slow ;  but  when  the  temperature  is  raised  above  60° 
C.,  the  phosphorus  ignites.  There  is  some  reaction  taking 
place  below  the  ignition  temperature,  but  it  is  slow,  and  in 
most  cases  the  reaction  is  so  slow  that  it  cannot  be  observed. 
The  reaction  velocity  at  the  ignition  temperature  is  so  great 
that  the  heat  evolved  is  sufficient  to  maintain  this  tempera- 
ture and  even  increase  it  with  the  accompanying  increase  in 
the  speed  of  the  reaction.  In  many  cases  a  small  rise  in  tem- 
perature may  then  give  an  enormous  increase  in  the  velocity 
of  the  reaction.  Cane  sugar  is  inverted  about  five  times  as 
fast  at  55°  as  at  25°.  According  to  Berthollet  an  ester  may 
be  formed  about  twenty-two  thousand  times  as  fast  at  200° 
as  at  7°.  Many  empirical  formulations  of  the  change  of  the 


496 


PHYSICAL   CHEMISTRY 


velocity  of  a  reaction  with  the  temperature  have  been  made. 
The  relation  seems  to  be,  that  the  velocity  is  nearly  propor- 
tional to  the  square  root  of  the  absolute  temperature. 

The  influence  of  pressure  on  the  velocity  of  reaction  is  prac- 
tically negligible  in  the  case  of  reactions  of  the  first  order, 
but  for  reactions  of  the  second  order  the  effect  is  nearly  a 
linear  function  of  the  pressure.  The  velocity  of  decomposi- 
tion of  hydriodic  acid  is,  according  to  Bodenstein,  practi- 
cally proportional  to  the  pressure  to  which  the  gas  is  sub- 
jected. The  reaction  between  metals  and  acids  with  the 
liberation  of  hydrogen  ceases  above  a  certain  pressure, 
according  to  Nernst  and  Tammann. 

The  nature  of  the  medium  in  which  a  chemical  reaction  takes 
place  has  a  marked  effect  on  the  velocity  of  the  reaction. 
Menshutkin  gives  the  data  in  Table  XC  for  the  velocity  con- 
stant in  a  number  of  solvents  for  the  reaction  of  ethyliodide 
on  triethylamine, 

C2H5I  +  (C2H5)3N  :£  (C2H5)4NI 
TABLE  XC 


SOLVENT 

VELOCITY 

DIELECTRIC  CONSTANT 
OF  SOLVENT 

.Xylene                                     «    •»• 

O  00287 

2  6 

Benzene         *"->* 
Ethyl  alcohol     
Methyl  alcohol 

0.00584 
0.0366      . 
o  0516 

2.26 
20.5 

\3.2 

Acetone    
Acetophenone 

0.0608 

O  I2Q4. 

21.5 

18.1 

Benzyl  chloride       

O.I^O 

10.6 

This  illustrates  the  marked  change  in  the  velocity  of  the 
reaction  with  change  of  solvent.  Various  efforts  have  been 
made  to  connect  this  with  the  different  physical  properties 
of  the  solvent,  —  such  as  the  dielectric  constant,  viscosity, 
dissociation  power,  etc.  The  value  of  the  dielectric  constant 


RATE  OF  CHEMICAL  REACTIONS  497 

for  the  solvents  is  given  in  the  last  column  of  the  table.  The 
velocity  constants  do  not  appear  to  bear  any  relation  to  the 
dielectric  constant  of  the  solvent  or  to  the  viscosity  changes. 
From  the  evidence  available  the  physical  properties  of  the 
solvents  alone  do  not  seem  to  determine  the  reaction  velocity, 
but  it  is  to  be  noted  that  those  solvents  with  high  dissocia- 
tive power  are  the  ones  in  which  the  reaction  of  dissolved 
substances  is  the  most  pronounced. 

In  the  reaction  of  hydrogen  and  oxygen,  as  in  the  case  of  the 
ignition  of  other  gases,  there  is  a  definite  rate  at  which  the 
flame  travels  throughout  the  mass  of  gas.  The  ignition  is 
started  at  one  point  and  owing  to  the  intense  heat  developed, 
due  to  the  chemical  reaction  of  the  gases,  there  is  an  increase 
in  pressure.  The  time  required  to  develop  the  maximum 
pressure  is  then  a  measure  of  the  explosiveness  and  is  the 
time  of  explosion.  The  explosion  is  considered  complete  when 
maximum  pressure  is  reached.  Bunsen  found  that  for 
oxygen  and  hydrogen  maximum  pressure  was  attained  in 
-^oVo  of  a  second  and  the  high  temperature  lasted  for  at 
least  ^3-  of  a  sceond.  The  temperature  obtained  by  calcu- 
lation necessary  to  produce  this  pressure  was  2500°.  But 
making  corrections  for  steam  condensed  the  value  found  was 
3897°,  but  on  further  corrections  for  heat  evolved  by  the 
combustion,  which  was  assumed  complete  before  maximum 
pressure  was  reached,  constant  specific  heat  of  steam  at  con- 
stant volume,  etc.,  assuming  ideal  conditions,  the  value  of 
9000°  was  found.  But  these  ideal  conditions  are  unattain- 
able, and  the  maximum  temperature  ranges  between  2500° 
and  3900°,  which,  however,  does  not  account  for  all  of  the 
heat  evolved.  As  the  ignition  of  the  mixture  takes  place 
from  particle  to  particle,  the  heat  due  to  the  reaction  causes 
an  expansion,  which  in  turn  causes  the  projection  of  the  ig- 
nited into  the  unignited  particles  and  increases  the  rate  of 
ignition. 

The  formation  of  these  gases  is  so  violent  that  their  quick 


498  PHYSICAL  CHEMISTRY 

expansion  produces  another  blow  on  the  surrounding  mass, 
which  causes  complete  explosion  of  the  entire  mass.  The 
rise  of  pressure  is  exceedingly  rapid  and  produces  not  only 
a  forward  wave  of  detonation  but  also  a  sudden  backward 
wave  of  compression  which  hastens  this  residual  combustion. 
The  explosive,  or  detonating  wave  set  up  is  comparable  to  a 
sound  wave  passing  through  a  gaseous  mixture.  It  results, 
however,  from  "  an  abrupt  change  in  chemical  condition 
which  is  propagated  in  the  explosive  wave  and  which  gener- 
ates an  enormous  force  as  it  passes  through  successive  layers 
of  the  media."  Berthelot  considers  that  the  main  velocity 
of  translation  of  the  molecules  of  the  products  of  combustion, 
retaining  kinetic  energy  corresponding  to  the  heat  developed 
in  the  reaction,  may  be  regarded  as  the  limiting  maximum 
rate  of  propagation  of  the  explosive  wave.  Berthollet  and 
Vieille  found  the  rate  of  propagation  of  the  explosive  wave 
in  pure  electrolytic  gas  to  be  2810  meters  per  second,  and 
Dixon's  value,  2819  meters  per  second,  confirmed  this. 

Catalysis.  —  The  inversion  of  cane  sugar  is  much  more 
rapid  in  the  presence  of  acids  than  in  pure  aqueous  solution, 
and  we  have  seen  that  the  rate  of  inversion  is  proportional  to 
the  concentration  of  the  acid,  i.e.  to  the  concentration  of  the 
hydrogen  ions.  The  hydrogen  does  not  enter  into  the  prod- 
ucts of  the  reaction,  but  its  presence  greatly  accelerates  the 
progress  of  the  reaction.  Berzelius  introduced  the  term 
catalytic  agent  and  defined  it  as  follows  :  "  A  catalytic  agent 
is  a  substance  which,  merely  by  its  presence  and  not  through 
its  affinity,  has  the  power  to  render  active,  affinities  which 
are  latent  at  ordinary  temperature."  The  agent  which 
causes  the  catalytic  action  or  catalysis  is  called  a  catalyzer  or  a 
catalyst.  Ostwald  defines  a  catalytic  agent  as  a  substance 
which  affects  the  velocity  of  a  chemical  reaction  without  it- 
self appearing  in  the  final  product. 

A  catalyzer  cannot  start  a  reaction,  but  it  merely  modifies 
the  velocity  of  the  reaction.  It  does  not  change  the  equilib- 


RATE   OF   CHEMICAL   REACTIONS  499 

rium  point,  as  it  affects  the  velocity  of  the  inverse  reactions 
to  the  same  degree.  There  is  no  change  in  the  concentration 
of  the  catalyst,  for  if  in  the  inversion  of  cane  sugar  by  means 
of  acid,  the  concentration  of  the  acid  be  ascertained  at  differ- 
ent stages  of  the  reaction,  the  values  will  all  be  the  same. 
An  infinitely  large  quantity  of  the  reacting  substances  can  be 
transformed  by  a  very  small  quantity  of  the  catalyzing  agent. 
Titoff  says  that  the  rate  of  oxidation  of  a  solution  of  sodium 
sulphite  is  noticeably  increased  by  even  dipping  a  strip  of 
clean  copper  into  the  solution  for  a  few  seconds.  The  re- 
duction of  mercuric  chloride  by  oxalic  acid  is  greatly  in- 
creased by  the  addition  of  potassium  permanganate  to  a  con- 
centration of  o.ooooo i  gram  in  ten  cubic  centimeters.  The 
nature  and  the  quantity  of  the  catalyst  does  not  affect  the 
finaf  state  of  an  equilibrium.  There  are  a  large  number  of 
catalytic  agents  and  reactions,  and  Ostwald  goes  so  far  as  to 
state  that  "  there  is  probably  no  kind  of  chemical  reaction 
which  cannot  be  influenced  catalytically,  and  there  is  no 
substance,  element,  or  compound  which  cannot  act  as  a 
catalyzer."  Although  there  have  been  several  efforts  to 
classify  catalytic  reactions,  we  shall  not  present  any  of  these, 
but  shall  consider  a  few  of  the  marked  examples  of  catalysis 
and  mention  a  few  technical  applications  of  catalytic  reac- 
tions. 

On  placing  a  platinum  wire  heated  to  redness  in  various 
mixtures  of  gases  and  vapors  combination  results.  This 
was  shown  by  Humphry  Davy  (1817),  and  this  fact  was  uti- 
lized by  Hempel  for  the  analysis  of  mixtures  of  gases.  By 
passing  a  mixture  of  oxygen  with  hydrogen,  carbon  monoxide, 
methane,  and  nitrogen  over  spongy  platinum  at  177°,  only 
the  hydrogen  and  the  carbon  monoxide  are  oxidized.  Phillips 
in  1831  patented  the  method  for  manufacturing  sulphuric 
acid  by  the  process  of  oxidizing  SOz  with  the  use  of  platinum 
wire  or  platinum  sponge.  But  owing  to  the  fact  that  certain 
impurities  destroyed  the  catalytic  action  of  the  platinum  the. 


500  PHYSICAL  CHEMISTRY 

process  was  abandoned.  A  number  of  substances  such  as 
hydrogen  sulphide,  ammonia,  ethylene,  etc.,  have  been  found 
to  destroy  or  inhibit  the  activity  of  the  platinum. 

The  more  highly  dispersed  the  catalyst  is,  the  greater  its 
chemical  activity.  For  example,  platinum  black  is  more 
active  than  sheet  platinum,  i.e.  there  is  more  surface  exposed. 
Mitscherlich  concludes  that  "  the  layer  of  carbon  dioxide 
which  condenses  on  the  walls  of  wood  charcoal  is  about 
0.00005  cm-  thick,"  and  that  at  least  one  third  of  the  carbon 
dioxide  so  condensed  is  in  the  liquid  state.  That  perfectly 
dry  gases  do  not  unite  has  been  demonstrated  by  a  number 
of  investigators.  Dixon  (1880)  demonstrated  that  the  reac- 
tion takes  place  only  in  the  presence  of  moisture  and  showed 
that  at  100°  sulphur  dioxide  and  oxygen  will  not  unite  in  the 
presence  of  water  vapor,  but  that  a  particle  of  liquid  water 
produces  oxidation.  This  condensation  theory  of  combus- 
tion proposed  by  Faraday  has  been  supported  by  many  others 
and  particularly  by  Dixon,  who  attributes  to  water  vapor 
the  r61e  of  an  "  oxygen  carrier."  This  was  stated  by  Mrs. 
Fulhame  in  1794,  nearly  a  century  before,  as  follows  :  "  Water 
is  essential  for  the  oxidation,  and  it  is  always  decomposed  in 
the  process;  .  .  .  carbon  monoxide  unites  with  the  oxygen 
of  the  water,  while  the  hydrogen  of  the  latter  seizes  the  oxy- 
gen of  the  air."  Dixon  showed  that  when  the  vapors  such  as 
hydrogen  sulphide,  ammonia,  formic  acid,  ethylene,  etc.,  were 
mixed  with  oxygen  and  carbon  monoxide  the  explosion 
would  take  place,  while  if  carbon  dioxide,  nitrogen  monoxide, 
and  carbon  bisulphide  were  employed  no  explosion  resulted. 
Hence,  not  only  steam  but  all  substances  which  will  form  steam 
under  the  conditions  of  the  experiment  will  cause  the  reaction 
to  take  place. 

A  minute  portion  of  the  solid  phase  of  the  solute  introduced 
into  a  supersaturated  solution  of  this  particular  solute  may 
cause  the  mass  to  crystallize ;  the  blow  by  a  trigger  causes 
the  materials  in  the  detonator  to  react ;  and  similarly  the 


RATE  OF   CHEMICAL  REACTIONS  501 

addition  of  small  amounts  of  material  or  small  amounts  of 
energy  in  various  forms  such  as  heat,  light,  etc.,  may  result 
in  chemical  changes  which  produce  enormous  quantities  of 
energy  in  other  forms.  These  results  are  not  at  all  commen- 
surate with  the  initial  inaugurating  effect  and  are  independ- 
ent of  it.  Phenomena  of  this  type  must  be  clearly  different 
from  what  is  termed  catalysis,  but  it  is  not  an  easy  matter 
to  distinguish  the  differences. 

Catalytic  Processes.  —  There  are  a  large  number  of  reac- 
tions which  we  term  catalytic  for  which  no  very  satisfactory 
explanation  had  been  presented,  and  the  method  of  the  reac- 
tion has  been  "  explained  "  by  stating  that  it  was  catalytic, 
which  of  course  does  not  "  explain."  Efforts  have  been  made 
to  show  how  the  catalyst  actually  takes  part  in  the  reaction, 
and  the  "  combination  hypothesis  "  as  employed  by  Dixon 
is  extensively  used.  This  is  analogous  to  the  explanation  of 
the  electrolytic  decomposition  of  water.  We  use,  however, 
either  an  acid  or  an  alkaline  solution  and  obtain  hydrogen  and 
oxygen,  the  constituents  of  water.  In  the  catalytic  action  of 
dilute  acids  Kastle  and  other  workers  state  that  the  hydrogen 
ions  react  first  to  form  addition  products,  and  these  subse- 
quently are  decomposed  into  the  final  products.  In  the 
Friedel  and  Crafts'  reaction  anhydrous  aluminium  chloride  is 
used  as  the  catalytic  agent.  The  reaction  is  explained  usu- 
ally by  assuming  the  formation  of  additive  intermediate  com- 
pounds, which  then  react  to  reform  the  catalytic  agent  alu- 
minium chloride.  The  reaction  between  benzene  and  ethyl 
chloride  is  explained  as  follows  : 

A12C16  +  C6H6  =  A12C15  •  C6H5  +  HC1 
and    A12C15  •  C6H5  +  C2H5C1  =  A12C16  +  C6H5  •  C2H5. 

The  aluminium  chloride  reacts  with  the  benzene,  and  this 
intermediate  compound  then  reacts  with  the  ethyl  chloride 
with  the  reformation  of  aluminium  chloride. 

The  manufacture  of  chlorine  by  the  Deacon  Process  is 


f 

502  PHYSICAL   CHEMISTRY 

usually  explained  chemically  by  assuming  the  formation  of 
intermediate  products.  Thus, 

CuSO4  +  2  HC1  =  CuCl2  +  H2SO4 

2  CuCl2  =  2  CuCl  +  C12 
4  CuCl  +  O2  =  2(CuCl2  +  CuO) 
CuCl2  +  CuO  +  2  HC1  =  2  CuCl2  +  H2O 

The  copper  acting  as  a  carrier  of  the  chlorine,  we  have  the 
formation  of  cupric  chloride,  its  decomposition  into  cuprous 
chloride  with  liberation  of  chlorine,  and  then  its  subsequent 
regeneration  in  the  presence  of  hydrochloric  acid.  The  ex- 
planation that  the  copper  salt  is  a  "  contact  agent  "  which 
aids  in  attaining  the  equilibrium  2  HC1  +  O2  $  H2O  +  2  CU 
is  also  offered. 

Metallic  Catalysts.  —  Platinum  in  a  very  fine  state  is  em- 
ployed in  many  catalytic  processes,  and  it  has  been  found  that 
numerous  other  metals  as  well  as  their  oxides  can  be  employed 
in  a  large  number  of  reactions  in  order  to  increase  the  velocity 
of  the  reaction  to  such  an  extent  that  it  can  be  carried  on 
under  normal  conditions  (which  include  lower  temperature) 
with  the  insurance  of  a  large  yield  of  the  desired  product 
and  the  financial  success  of  the  process. 

In  addition  to  platinum  may  be  mentioned  finely  divided 
indium,  palladium,  osmium,  copper,  iron,  nickel,  cobalt,  vana- 
dium, ruthenium,  and  the  oxides  of  the  same  ;  colloidal  sus- 
pensions of  metals  have  proved  excellent  catalyzers.  Cerium 
was  used  as  catalyst  for  combining  hydrogen  and  nitrogen 
to  make  ammonia,  but  iron  is  extensively  used  for  that  pur- 
pose. Electrolytic  cerium,  mixed  with  about  two  per  cent  of 
potassium  nitrate  when  employed  as  a  catalytic  agent  for  the 
combination  of  hydrogen  and  nitrogen,  gave  about  three  times 
the  yield  of  the  untreated  cerium.  Substances  of  this  type 
are  designated  promoters.  In  general,  the  compounds  of  the 
metals  of  the  alkali  and  the  alkaline  earths  are  promoters  of 
catalytic  action,  as  well  as  the  oxides  of  the  rare  earth  metals 


RATE  OF  CHEMICAL  REACTIONS  503 

tantalum  and  niobium,  as  well  as  silica,  while  the  metal- 
loids, sulphur,  selenium,  tellurium,  arsenic,  phosphorus,  and 
easily  fusible  and  easily  reducible  metals  such  as  zinc,  lead, 
and  tin,  usually  act  as  contact  poisons. 

There  are  two  of  these  used  in  extensive  industrial  pro- 
cesses which  will  be  considered  in  some  detail.  They  are 
platinum  in  the  contact  process  for  the  manufacture  of  sul- 
phuric acid  and  nickel  in  the  hydrogenation  of  oils. 

The  Hydrogenation  of  Oils.  —  The  addition  of  hydrogen 
to  oleic  acid  (CigH^C^)  with  the  formation  of  stearic  acid 
(Ci8H36O2)  has  been  one  of  the  problems  of  the  chemist  for 
years.  Oleic  acid  is  a  liquid  and  stearic  acid  is  a  solid  at  ordi- 
nary temperatures.  This  fact,  in  addition  to  the  great 
abundance  of  oleic  acid,  made  it  desirable  to  utilize  oleic 
acid  as  a  source  of  hard  fats.  Lewkowitsch  as  late  as  1897 
states  that  while  the  lower  members  of  the  oleic  acid  series 
can  be  converted  into  saturated  acids,  "  oleic  acid  itself  has 
resisted  all  attempts  at  hydrogenation."  It  was  not  until 
about  ten  years  later  (1907)  that  Bedford  and  Williams  pub- 
lished the  first  description  of  a  method  of  exposing  oil  to  the 
action  of  hydrogen  by  forming  the  oil  in  a  spray  or  film  in 
an  atmosphere  of  hydrogen  in  contact  with  a  catalyzer  of 
nickel.  They  converted  linseed  oil  into  a  hard  fat  melting 
at  53°,  oleic  acid  into  stearic  acid  with  a  melting  point  of  69°, 
and  the  solidifying  point  of  paraffin  wax  was  raised  3°.  While 
this  is  still  the  general  method  employed  in  the  hydrogena- 
tion of  oils,  many  detailed  mechanical  devices  have  been 
introduced. 

Various  catalyzers  have  been  tried,  but  the  one  used 
principally  is  metallic  nickel,  and  numerous  patents  have  been 
issued  on  methods  for  the  preparation  of  the  catalytic  agent. 
An  effective  nickel  catalyzer  may  be  prepared  by  either  ig- 
niting nickel  nitrate  to  obtain  the  oxide,  or  by  precipitating 
the  nickel  hydroxide  from  a  sulphate  solution  by  an  alkali. 
This  oxide  or  hydroxide  is  then  reduced  by  hydrogen  at  a 


504  PHYSICAL   CHEMISTRY 

temperature  between  250°  and  500°  or  until  water  is  no  longer 
formed.  The  lower  the  temperature  at  which  the  reduc- 
tion takes  place,  the  more  sensitive  it  is ;  a  good  working 
range  is  between  300°  and  350°.  The  catalyzer  is  more  effi- 
cient when  the  active  surface  is  increased  by  employing  a 
carrier.  So  there  are  employed  a  large  number  of  carriers 
and  extenders,  such  as  pumice  stone,  kieselguhr,  charcoal, 
and  sawdust.  The  catalyzer  should  be  protected  from  the 
air  to  prevent  oxidation.  It  is  claimed  by  various  investi- 
gators that  a  short  period  is  required  for  the  nickel  catalyzer 
to  become  acclimated,  as  it  were,  before  reaching  its  maxi- 
mum efficiency  or  activity,  after  which  there  is  then  a  period 
of  decline.  The  most  active  period  is  generally  very  long,  and 
the  period  of  decline  is  usually  attributed  to  the  action  of 
poisons.  For  treating  liquids,  superficially  treated  or  coated 
carriers  are  most  desirable,  while  for  the  hydrogenation  of 
gases  or  vapors  porous  impregnated  catalyzers  are  better. 

The  Mechanism  of  Hydrogenation.  —  The  methods  by 
which  the  various  catalytic  metals  transfer  the  hydrogen 
during  the  process  of  addition  or  hydrogenation  of  numerous 
bodies,  as  well  as  the  reduction  by  hydrogen  of  other  bodies, 
has  led  to  many  attempted  explanations.  The  prevalent 
ones  are  the  adsorption  method  and  the  hydride  formation. 
Whether  the  hydrogen  is  adsorbed,  absorbed,  or  occluded, 
there  is  difference  of  opinion,  as  Firth  shows  that  adsorption 
of  hydrogen  by  wood  charcoal  takes  place  in  a  few  minutes, 
while  hours  are  required  for  an  equilibrium  to  be  realized  by 
absorption.  That  many  metals  dissolve  hydrogen  has  been 
demonstrated  by  many  workers,  and  in  Table  XCI  are  given 
the  volumes  of  hydrogen  under  normal  conditions  that  are 
adsorbed  by  one  volume  of  the  metal. 

The  adsorption  of  hydrogen  by  palladium  and  by  platinum 
is  very  pronounced,  and  the  same  is  true  for  cobalt,  nickel, 
and  iron.  The  solubility  increases  with  a  rise  in  tempera- 
ture, and  the  metals  copper,  iron,  and  nickel  in  the  liquid 


RATE  OF   CHEMICAL  REACTIONS  505 

state  manifest  a  very  marked  increase  in  solubility  with  in- 
crease in  temperature.  On  solidifying  at  1084°,  copper 
gives  up  twice  its  volume  of  hydrogen,  iron  at  1510°  about 
seven  times  its  volume,  and  nickel  at  1450°  about  12  times  its 
volume.  They  all  "  spit  "  when  allowed  to  freeze  in  an  at- 
mosphere of  hydrogen. 

TABLE  XCI  —  ADSORPTION  OF  HYDROGEN 

(Abegg  and  Auerbach)  Anorganischen  Chemie 


METAL 

VOLUME  OF  HYDROGEN 

Reduced  cobalt     ....... 
Precipitated  gold 

59-153 
•17—4.6 

Reduced  nickel           .               ... 

1  7—1  8 

Reduced  iron    

Q.4.-I9.2 

Cast  iron      
Sheet  aluminium 

0.57-0.8 
1.  1-2.  7 

IVlagnesium                 

1.4 

Silver  powder        
Reduced  copper 

0.91-0.95 

0.6-4..  8 

Copper  wire                          .... 

o.-* 

Silver  powder         

0.91-0.95 

Contact  Process  for  Manufacture  of  Sulphuric  Acid.  —  The 

reaction  between  sulphur  dioxide  and  oxygen  takes  place 
slightly  at  about  350°  to  375°  without  the  aid  of  a  catalyzer  ; 
but,  in  the  presence  of  a  catalyst,  platinum  black,  the  reac- 
tion begins  at  325°  and  the  rate  of  reaction  increases  so  that 
at  about  375°  to  450°  the  sulphur  dioxide  and  oxygen  com- 
bine readily  with  practically  the  theoretical  yield  of  sulphur 
trioxide.  Ferric  oxide  at  higher  temperatures  is  less  efficient 
as  a  catalyst,  while  other  catalysts,  such  as  ferric  oxide  con- 
taining a  little  copper  oxide,  chromium  oxide,  hot  silica,  and 
quartz,  are  even  less  efficacious. 
According  to  the  law  of  mass  reaction  we  have,  from  the 

equilibrium    equation,    2  SO*  +  02  ^  2  SOs,  Kp  =  -     s°3 

~ 


PHYSICAL  CHEMISTRY 


in  which  KP  is  the  equilibrium  pressure  constant.  The  values 
of  this  constant  with  increase  in  temperature  are  given  (by 
Bodenstein)  as  follows : 


Degree   C.     . 

450 

528 

579 

627 

680 

727 

789 

832 

897 

KP        ... 

188 

31-3 

13-8 

5-54 

3-24 

1.86 

0.956 

0.627 

0.358 

By  the  use  of  platinum  black  as  a  catalyst  the  reaction  can 
be  noticed  at  a  temperature  as  low  as  200°  ;  the  rate  of  reac- 
tion becomes  very  rapid  above  450°.  The  heat  of  this  reac- 
tion is  21.6  calories,  and  the  heat  obtained  from  the  rapid 
formation  of  SO3  results  in  the  rise  of  temperature  unless 
proper  provisions  are  made  to  keep  the  temperature  constant 
at  about  450°  by  dilution  of  gases  and  absorption  of  heat, 
otherwise  there  will  be  reversal  of  the  reaction.  The  values 
of  Kp  indicate  that  the  dissociation  of  the  SO3  increases  rap- 
idly with  rise  of  temperature,  and  a  small  rise  in  tempera- 
ture reduces  the  yield  of  SO3.  This  reversal  of  the  equilib- 
rium and  the  inhibiting  or  poisoning  action  of  the  impurities 
in  the  gases  from  the  burners  used  in  producing  the  SOz 
from  iron  pyrites  were  two  factors  which  retarded  the  success- 
ful commercial  utilization  of  this  method  for  the  manufac- 
ture of  sulphuric  acid. 


APPENDIX    . 

To  supply  the  data  for  numerous  problems  such  as  are 
required  for  use  with  large  classes  necessitates  many  duplica- 
tions, and  in  most  lists  of  problems  but  few  of  the  same 
type  are  given.  To  multiply  these  as  usually  stated  requires 
considerable  space,  and  as  this  has  not  been  done  there  is  a 
demand  for  more  illustrative  material.  We  have  endeavored 
to  provide  this  material  in  the  tables  compiled  in  this  Ap- 
pendix, which  affords  material  for  the  problems  illustrating 
the  fundamental  principles  given  in  the  text. 

The  principal  formulae  have  been  collected  under  the 
different  headings,  and  as  supplementary  to  the  subject 
matter  of  the  text  are  used  to  indicate  the  method  of  solution 
of  the  problems,  instead  of  giving  type  solutions. 

Instead  of  expressing  in  words  the  conditions  of  a  problem, 
the  data  have  been  arranged  in  tabular  form,  and  the  instruc- 
tor can  clothe  the  data  in  the  form  he  may  desire.  This 
method  of  presentation  has  several  advantages,  one  of  which 
is  compactness,  and  another  is  that  the  answers  appear 
as  one  of  the  terms  in  the  table.  For  instance,  in  the  Gas 
Law  Equation  pV  =  nRT,  there  are  five  terms,  any  one  of 
which  may  be  assumed  unknown ;  with  the  others  known 
the  value  of  the  one  unknown  is  the  answer  to  the  specified 
problem  formulated  in  any  appropriate  terms. 

Another  illustration  will  suffice  to  represent  the  general 
plan  of  the  arrangement  and  the  method  of  employing  the 
data  tabulated.     Take  the  first  problem  in  Table  XX,  C, 
53  4»  which  as  stated  in  the  usual  manner  would  read  : 
507 


508  PHYSICAL  CHEMISTRY 

The  specific  conductance  of  a  5  per  cent  solution  of  HC1 
at  1 8°  is  0.3948  mho.  If  the  equivalent  conductance  at 
infinite  dilution  A^  is  376,  calculate  the  degree  of  dissociation. 
Also  calculate  the  freezing  point  of  the  solution.  Calculate 
the  vapor  pressure. 

As  tabulated  there  are  the  following  terms :  the  specific 
conductance  *,  the  per  cent  composition,  the  density  p,  the 
value  of  A,*,,  all  of  which  may  be  considered  the  known  data 
from  which  the  degree  of  dissociation  a,  the  freezing  point, 
and  the  vapor  pressure  may  be  calculated,  and  may  be 
termed  the  answers. 

1.  To  calculate  the  degree  of  dissociation  a,  AF  must 
first  be  obtained  from  V  and  K  ;   but  V  is  obtained  from 
p  and  the  per  cent  composition.     Now  knowing  AF  and 
A^,  a  is  readily  calculated. 

2.  With  the  data  given,  the  freezing  point  and  the 
vapor  pressure  of  the  solution  may  be  calculated. 

Now,  considering  these  answers  as  part  of  the  given  data, 
other  problems  which  illustrate  the  principles  involved 
equally  as  well  as  the  above  problems  may  be  formulated, 
and  the  answers  appear  in  the  table.  A  few  of  these  may  be 
outlined. 

3.  Given  the  vapor  pressure  and  the  concentration, 
calculate  the  degree  of  dissociation  and  the  freezing 
point  of  the  solution. 

4.  Given  the  freezing  point  and  the  concentration, 
calculate  the  degree  of  dissociation  and  the  vapor  pres- 
sure of  the  solution. 

5.  Select  the  proper  data  and  calculate  the  concen- 
tration of  the  solution  from  the  freezing  point,  the  vapor 
pressure,  and  the  electrical  conductance  of  the  solution. 

6.  Calculate    the    specific    conductance,    given    the 
concentration  of  the  solution. 

From  the  data  tabulated  in  these  ten  problems,  we  not 
only  have  thirty  problems  on  the  basis  that  the  values  in  the 


APPENDIX 


509 


last  three  columns  are  the  answers,  but  as  indicated  above, 
we  could  have  all  together  over  one  hundred  problems.  The 
same  holds  for  the  other  tables.  We  have  a  great  variety 
offered,  with  the  answers  in  one  of  the  columns. 

TABLE  I 
Percentage  Composition  and  Formula 

The  formula  of  a  compound  is  a  combination  of  symbols 
that  represents  the  percentage  composition  of  the  compound 
and  such  that  the  formula  weight  in  grams  of  the  compound 
in  the  gaseous  state  occupies  22.4  liters  of  space  under 
standard  conditions.  If  the  compound  cannot  be  obtained 
in  the  gaseous  state,  then  other  facts  are  used,  such  as  the 
effect  of  the  compound  upon  a  solvent  in  lowering  the  vapor 
pressure,  lowering  the  freezing  point,  raising  the  boiling  point. 
In  general,  the  formula  of  a  compound  is  obtained  by  the 
following  rule : 

Use  the  simplest  combination  of  symbols  that  represents  the 
percentage  composition  of  the  compound  and  agrees  with  the 
known  facts. 


APPROXIMATE  WT. 

PERCENTAGE 

COMPOSITION 

OF  i  LITER  AS  GAS 
UNDER  STANDARD 

CALCULATE 
FORMULA 

CONDITIONS 

I. 

Ba 

=  58.9 

S 

_ 

13-7 

0 

=  274 

BaSO4 

2. 

Mg 

=  21.8 

P 

= 

27.8 

0 

=  50.4 

Mg2P2O7 

3- 

Pb 

=  64.1 

Cr 

= 

16.1 

O 

=  19.8 

PbCrO4 

4- 

K 

=  16.0 

Pt 

= 

40.4 

Cl 

=  43-6 

K2PtCl6 

5- 

C 

=  64.9 

H 

= 

13-5 

O 

=  21.6 

3-33  g. 

(C2H5)20 

6. 

C 

=  54-5 

H 

= 

9.1 

O 

=  36.4 

3-96 

CH3C02C2H5 

7- 

C 

=  92.4 

H 

= 

7.6 

3.51 

C6H6 

8. 

C 

=  77-5 

H 

= 

7-5 

N 

=  15-0 

4.19 

CflH6NH2 

9- 

C 

=  62.1 

H 

= 

27.6 

O 

=  10.3 

2.62 

CH3COCH3 

10. 

C 

=  22.7 

H 

= 

6.6 

As 

=  70.7 

4.87 

(CH3)2AsH 

ii. 

C 

=  28.1 

O 

•B 

37-5 

Ni 

=  34-4 

770 

Ni(CO)4 

12. 

C 

=  38.8 

H 

= 

8.2 

Zn 

=  53-o 

5-54 

Zn(C2H5)2 

510  PHYSICAL  CHEMISTRY 

TABLE  II 
The  Gas  Law  Equation 

The  Gas  Law  Equation  pV  =  nRT  which  expresses  the 
relationship  of  the  mass,  pressure,  temperature,  and  volume 
of  a  gas  may  be  utilized  in  solving  problems  involving  these 
variables. 

For  a  given  gas  we  then  have 

a 

pV  =  nRT,  or  pv  =  rT,  in  which  R  =  mr  and  n  =  - 

m 


(a)  Or  if  any  three  of  the  values  g,  V,  T,  and  p  are  known, 
the  other  may  be  calculated. 

(b)  For  a  constant  mass  of  gaseous  substances  which  would 
occupy  a  volume  of  V,  at  the  temperature  /,  and  pressure  p, 
either  V2,  t2,  or  pz  may  be  readily  obtained  if  the  other  two 
are  known. 

The  data  for  problems  given  in  the  following  tables  are 
arranged  so  that  the  values  describing  the  conditions  under 
which  the  gas  exists  are  designated  by  the  same  subnumbers. 

In  Table  II  problems  might  read  : 

1.  What  will  be  the  volume  of  —  grams  of  —  at  20°  C. 
and  under  a  pressure  of  750  mm.  ? 

2.  At  what  temperature  will  —  grams  of  --  occupy 
a  volume  of  —  liters  under  a  pressure  of  750  mm./ 

j.  Under  what  pressure  will  —  g-  of  —  occupy  a 
volume  of  —  liters  at  temperature  t  ? 

4.  How  many  grams  of  —  will  be  required  to  occupy 
a  volume  of  —  liters  at  20°  C.  under  a  pressure  of 
750  mm.  ? 

Or  these  same  problems,  assuming  that  the  condition  desig- 
nated by  the  subscript  i  are  known, 


APPENDIX  511 

1.  To  what  t2  must  the  gas  be  raised  so  that  it  will 
occupy  a  volume  V2  at  the  pressure  p2  ? 

2.  If  the  gas  is  heated  to  a  temperature  t2,  what  vol- 
ume will  it  occupy,  V2,  if  the  pressure  is  p2  ? 

j.    To  what  pressure  must  the  gas  be  subjected  so 
that  its  volume  will  be  V2  at  t2  ? 

Or  the  values  indicated  by  the  subscript  2  may  be  assumed 
to  be  the  known  values  and  in  the  manner  just  indicated  the 
values  marked  by  the  subscript  i  calculated. 


SUBSTANCE 

GRAMS 

Pi 

Vi 
LITERS  * 

h 

/* 

V, 
LITERS 

h 

i.   Methane       .     .     . 

0.163 

745  mm. 

250  cc. 

20° 

760  mm. 

29.1  cc. 

75° 

2.   Ammonia     .     .     . 

8.20 

750  mm. 

12 

27 

740  mm. 

iS-i 

100 

3.    Sulphur  dioxide     . 

1.018 

740  mm. 

500  cc. 

100 

755  mm. 

42.1  cc. 

47 

4.   Argon      .... 

15.8 

5  atmos. 

2 

35 

25  atmos. 

3-74 

IS 

5.   Oxygen    .... 

20.9 

2  atmos. 

10 

100 

15  atmos. 

2.76 

500 

6.   Hydrochloric  acid  . 

164.6 

5  atmos. 

35 

200 

2  atmos. 

74.0 

127 

7.   Nitrogen       .     .     . 

0.2713 

725  mm. 

250  cc. 

27 

755  m. 

298  cc. 

IOO 

8.   Hydrogen     .     .     . 

1.  211 

725  mm. 

15 

15 

545  m. 

18.0 

—  13 

9.   Carbon  dioxide 

1-275 

742  mm. 

750  CC. 

35 

760  m. 

130.8  cc. 

277 

10.   Air      

17-5 

755  mm. 

is 

17 

275  m. 

49-4 

87 

TABLE  III 
The  Gas  Law  Equation 


SUBSTANCE 

gi 

* 

Fi 
LITERS 

ti 

0 

P* 

Vi 
LITERS 

ft 

i.  Air       .     . 

12.02 

i  atmos. 

10 

20° 

30.05 

25  atmos. 

10 

20° 

2.   Air  .     .     . 

83.9 

3.5  atmos. 

20 

21 

I2I.O 

5  atmos. 

20.2 

21 

3.   Hydrogen. 

22.55 

745  mm. 

300 

45 

16.6 

745  mm. 

200 

IS 

4.    COz      .     . 

9-13 

750  mm. 

5 

17 

10.5 

800  mm. 

5.5 

20 

Types.  —  Given  mass  at  p\  T\  V\,  find  change  in  one  term 
when  changes  in  other  three  are  known. 

*  Volume  in  liters  unless  otherwise  specified. 


PHYSICAL  CHEMISTRY 


TABLE  IV 
The  Specific  Gas  Constant 

Given  the  weight  of  one  liter  of  the  following  gases,  cal- 
culate the  specific  gas  constant,  r,  and  express  the  same  in 
liter-atmospheres  per  degree  and  in  gram-centimeters  per 
degree : 


'  i 

GAS 

LITER  IN  GRAMS 

In  Gram-cm,  per 
Degree 

In  Liter-atmos.  per 
Degree 

Nitrogen   

I.25I4. 

7Q2S 

.00292 

Argon 

I  782 

212  A. 

OO2O5 

Hydrochloric  acid  .     .     . 
Nitric  oxide  

1.6398 
I.IAO 

2310 
2825 

.00223 
.OO271 

Sulphur  dioxide  .... 
Oxygen      

2.9266 
1.429 

1293 
2652 

.00125 
.00256 

TABLE  V 
Specific  Gravity  and  the  Specific  Gas  Constant 

Given  the  specific  gravity  of  the  following  gases,  calculate 
the  specific  gas  constant,  r,  and  express  as  in  preceding : 


r 

c                r> 

GAS 

(AlR=l) 

In  Gram-cm,  per 

In  Liter-atmos.  per 

Degree 

Degree 

I.   Xenon  .... 

4.526 

647.5 

.000626 

2.   Chlorine     . 

2.491 

II77.0 

.001137 

3.   Ethane  .... 

1.0494 

2790.0 

.OO270 

4.   Arsine    .... 

2.696 

1087.0 

.001050 

5.    Methane    .     .     . 

0.5576 

5255.0 

.00508 

APPENDIX 


513 


TABLE  VI 

Molecular  Weight  and  Formula 

Calculate  the  molecular  weight  or  obtain  the  formula. 

g 
These  may  all  be  solved  from  pV  =  nRT  and  n  =  — . 


SUBSTANCE 

WEIGHT 

F! 

Pi 

h 

m 

I     Acetone   . 

0.1845 

o  6520 

81.5  cc. 

244.2 
242.1 
147.2 
76.5 

36.0 
272.O 

255-6 
232.5 

252.5 

732-3 

747-3 
754-4 
754-6 
735-6 

741.2 
761.4 

754-5 
759 

760.9 

26.8° 

59-8 
76.0 
72.6 
27.2 

24.8 
76.8 

1  80 

98.6 

78.2 

57-8 
74.2 

77-9 
118.5 
46.2 

FORMULA 
C6H6 

CH3CH2CHO 

C5H702CH8 
CeHi4 

CHC1, 

2.   Ether        

3     Benzene 

o  6^^o 

4     Chloroform 

o  61  1  1 

5.    Ethyl  alcohol     .... 
PERCENTAGE  COMPOSITION 
I.    C  =  92.3     H  =  7.7   .      . 
2.   C  =  62.07    O  =  27.59 
H  =  10  34          ... 

0.1390 
0.1123 

O  5S'?c\ 

3.   C  =  62.1     O  =  27.6 
H  =  10.3       .... 
4.   C  =  83.73     H  =  16.27  . 
5.   C  =  10.05     H  =  0.85 
Cl  =  89.1       .... 

0.788 
0.6590 

1.039 

TABLE  VII 
Dissociation  of  Gases 

By  employing  the  Mass  Law  Equation  and  Dalton's  Law, 
together  with  the  equations  m  =  s  X  m,  and  a  =      s  ~  Sl 


calculate  the  degree  of  dissociation  and  the  final  partial  pres- 
sures. Then  from  the  gas  equation  pV  =  nRT  calculate 
the  final  concentrations. 


'  •    .  • 

PHYSICAL   CHEMISTRY 


Dissociation  of  PC15  under  Atmospheric  Pressure 


PARTIAL  PRESSURES 

CONCENTRATIONS 

ATMOSPHERES 

MOLES  PER  LITER 

TEMP. 

s  (AIR) 

a 

PCls 

PCb  and  Cb 

PCls 

PCls  and  Clj 

I.    182 

5-08 

0.417 

0.4110 

0.2945 

O.OIIO 

0.0079 

2.    190 

4-99 

0-443 

0.3860 

0.3070 

0.0102 

O.OOSl 

3.    200 

4-85 

0.485 

0.3470 

0.3265 

0.0089 

0.0084 

4-    230 

4-30 

0.675 

0.1940 

0.4030 

O.OO47 

0.0098 

5-   250 

4.00 

0.800 

O.IIII 

0.4444 

O.OO26 

O.OIO4 

6.   274 

3-84 

0.875 

O.O667 

0.4665 

0.0015 

O.OIO4 

7.   288 

3-67 

0.962 

0.0194 

0.4903 

O.OOO4 

0.0107 

8.    300 

3.65 

0-973 

0.0137 

0.4931 

0.0003 

O.OIO5 

TABLE  VIII 
Gaseous  Equilibrium 

Equilibrium  equations  involving  problems  of  the  type 
when  a  given  mass  of  gas  occupies  a  specified  volume  at  a 
certain  pressure  and  temperature  to  calculate  degree  of  dis- 
sociation and  partial  pressures. 


EQUILIBRIUM  EQUA- 
TION 

GRAMS 

Fi 
LITERS 

Pt 

fc 

p 
|.PER 
LITER 

a 

PARTIAL  PRESSURES 

pi 

/>2 

P3 

NHs 

C02 

i.  NH4C02NH2  7>* 

6.71 

8.8 

745 

180 

0.763 

0.85 

496.8 

248.4 

(solid) 

2  NH3  +  COs 

^ 

NaO4 

NOz 

2.     N2O4  ^       2  NO2 

3-29 

6.65 

182.7 

49-7 

0-495 

0.69 

33-5 

149.2 

1-30 

855  cc. 

497-8 

49-7 

1-527 

0-49 

170.3 

327-5 

0.762 

12.0 

26.8 

49-7 

0.0635 

0-93 

0.97 

25-83 

NOz 

NO 

02 

3.     2  NO2  ^ 

2.18 

2-35 

737-2 

279 

0.928 

0.130 

602.2 

90 

45 

2  NO  +02 

4-05 

7-25 

742-5 

494 

0-559 

0.565 

251-7 

327-2 

136.6 

APPENDIX 


515 


TABLE  IX 
Dissociation  of  NH4HS 

Assuming  NH4HS  to  be  a  solid  and  the  part  vaporized  to 
be  completely  dissociated : 

1.  From  the  mass  V  and  t  calculate  the  partial  pressures. 

2 .  Now  by  introducing  a  given  mass  of  one  of  the  products 
of  dissociation  compute  the  partial  pressures  and  the  per- 
centage of  the  original  NH4HS  which  remains  dissociated. 

3 .  Calculate  the  specific  gravity  with  respect  to  air  of  each 
of  the  mixtures. 


GRAMS 

PARTIAL 

PER  CENT 

REACTION 

MASS  IN 
GRAMS 

V 
LITERS 

t 

ADDED 

PRESSURES 

DISSO- 
CIATED 

VIR) 

NH3 

H2S 

NHa 

H2S 

a 

NH4HS  -?" 

2 

25-1° 

0 

o 

251.8 

251.8 

IOO 

0.534 

(solid)    "*~ 

1.382 

1.17 

318 

458 

54-9 

0.745 

NHa  +  H2S 

0-495 

417 

146 

59-2 

0.508 

0.315 

208 

294 

84.2 

0.570 

TABLE  X 
Dissociation  of  Hydriodic  Acid 

Assume  that  one  mole  of  the  original  substance  taken 
and  that  when  equilibrium  is  established  x  moles  have  been 
dissociated.  Since  one  mole  is  assumed,  the  value  of  x  is 
the  same  as  a,  the  degree  of  dissociation,  and  from  any 
number  of  moles,  n,  the  number  of  moles  dissociated,  x,  would 
equal  an.  The  equilibrium  equation  for  the  dissociation 
of  hydriodic  acid  is  2  HI  ^  I2  +  H2  or  HI  =  £  I,  +  \  H2. 


Show  that   the  dissociation  constant  is  k\ 


4d  -  " 


and 


PHYSICAL  CHEMISTRY 


k,  = 


a 


respectively.     The  equilibrium  equation  for 
2(1  -  a) 

the  dissociation  of  N2O4  is  N2O4;£:  2  N02  or  \  N2O4  ^±  NO2. 

A.  a2 

Show    that    the    dissociation    constant    is    ki  =  — and 

i  —  a 

k2  =  - — 2  a       respectively,  in  which  one  is  the  square  root 
(i  -  a)2 

of  the  other. 

From  the  following  data  for  hydriodic  acid  calculate  the 
degree  of  dissociation  a,  or  the  equilibrium  constant  kz  at  the 
different  temperatures,  assuming  that  the  value  of  a  is  known : 


/ 

a 

k* 

520 

0.245 

0.162 

500 

0.238 

0.156 

480 

0.232 

0.152 

460 

0.225 

0.145 

440 

0.219 

O.I4I 

420 

0.213 

0.135 

400 

0.208 

0.132 

380 

0.202 

0.127 

360 

0.197 

O.I22 

340 

0.192 

O.II9 

TABLE  XI 
The  Law  of  Mass  Action  and  Gaseous  Equilibrium 

Whitaker  and  Rittman  (Jour.  Ind.  Eng.  Chem.,  6,  383 
(1914)),  give  the  following  practical  illustration  of  the  signif- 
icance of  equilibrium  conditions  in  the  manufacture  of  blue 
water  gas.  Assume  a  theoretically  ideal  mixture  consisting 
of  50  per  cent  H2  and  50  per  cent  CO.  Pass  the  two  gases 
through  a  chamber  heated  to  700°  C.  (1290°  F.)  until  they 
reach  the  equilibrium  at  this  temperature  ;  what  are  the  re- 


APPENDIX  517 

suiting  gases  ?     K  at  this  temperature  is  in  the  neighborhood 
of  0.32. 

3  CO  +  H2  =  CO2  +  H2O  +  2  C  +  67750  cal. 
Under  equilibrium  conditions 

Let  x  —  volume  CO  2 
then  %  =  volume  H2O 
0.5  —  x  =  volume  H2 
°-5  —  3  x  =  volume  CO 
.*.  i  —  2  x  =  total  final  volume 

x  0.5  —  x 

=  Pcot 


I    —    2  X 

x  0.5  —  3  x 

-  =  £HJO      -  =  Pco 

I    —    2  X  I    —    2  X 

~  2  *)  =  0-22 


(0.5  -  3  * 
Solving,       x  =  0.069  =  6.9  per  cent 

2  x  =  gas  lost  in  reaction  =13.8  per  cent 

=  8  per  cent  CO2 


I    —   2  X         0.862 

x  0.060 


I    —    2  #          0.862 


=  8  per  cent  H2O 


—  =  ^  =  50  per  cent  H5 

2   X         0.862 


I.  From  the  principles  illustrated  in  the  solution  of  the 
problem  above,  apply  these  to  a  mixture  of  1000  cubic  feet 
each  of  carbon  monoxide  and  hydrogen,  assuming  that  no 
hydrocarbons  are  formed  and  that  there  is  a  net  loss  of  13.8 
per  cent  due  to  the  reaction ;  what  is  the  number  of  cubic 
feet  of  the  gaseous  constituents  and  the  number  of  pounds  of 
carbon  formed  ?  What  is  the  percentage  composition  of  the 
permanent  gas  and  how  many  cubic  feet  of  the  original  con- 
stituents remain  ? 


518  PHYSICAL   CHEMISTRY 

II.  If  i  liter  of  carbon  dioxide  is  passed  over  carbon  heated 
at  600°,  calculate  the  composition  of  the  resulting  mixture 
assuming  the  reaction  to  be  CO2  +  C  =  2  CO. 

K      -  (CO)'  _ 

K-  -       ' 


Let     2  x  =  volume  of  CO  Ans.  Final  volume  =  1.156  liter 

I  —  x  =  volume  of  CO2  volume  CO  =  0.312  liter 

percentage  CO  =  26.99 
i  +x  =  final  volume  percentage  CO2  =  73.01 

III.  If  i  liter  of  CO  forms  CO2  and  carbon  at  750°,  calcu- 
late the  percentage  composition  of  the  resulting  mixture  and 

(CO)2 

the  degree  of  dissociation.     KP=  v       '    =  3.94 

CO2 

Ans.    Percentage  dissociation  =  0.27     Percentage  CO  =  77.3 
Percentage  CO2  =  22.7 

IV.  Ethylene  dissociates  into  acetylene  and  hydrogen. 

C*  TT      TT 

The  values  for  the  equilibrium  constant  KP  =     2    *  —  -  at 

C2.H.4 

the  temperatures  600°,  750°,  and  900°  C.  are  0.00018,  0.0093, 
and  0.0178  respectively.  Calculate  the  volume  of  acetylene 
and  the  total  gas  volume  at  the  different  temperatures. 

600°  750°  900° 

Ans.      Volume  of  acetylene     ...     0.01342        0.09602        0.1323 
Total  volume      .     .     .     .     .     1.01342         1.09602         1.1323 

V.  If  0.5  liter  of  NO  and  0.5  liter  of  O2  are  allowed  to  come 
to  equilibrium  at  2195°  C.,  find  the  percentage  composition 
of  the  mixture. 

KP  =      PNO      =  0.0242 


Ans.     Degree  of  dissociation  a  =  0.0119     NO  =     1.19  per  cent 

O2  =  20.4    per  cent 
N2  =  77.4    per  cent 


APPENDIX 


519 


VI.   The  percentage  composition  of  mixtures  of  N2,  H2, 
and  NH3  is  given  in  the  following  table  : 


VOLUME  PER  CENT  or 

TEMP 

H2 

N2 

NHa 

27° 

2.76 

0.92 

96.32 

327 

73-75 

24.58 

1.67 

627 

74-97 

24.99 

0.039 

930 

75.00 

25.00 

0.0065 

Calculate  KP  at  27°  C.  and  at  930' 
technical  practice  ? 


Why  is  not  27°  used  in 


Ans.       27  KP  =  2.1.9.  X  io8 
930  KP  =  2.00  X  io~4 


VII.  Derive  an  equation  showing  how  the  degree  of  dis- 
sociation of  ammonia  may  be  calculated  at  any  other  pres- 
sure if  KP  at  one  pressure  for  a  given  temperature  is  known. 
KP  at  930°  under  i  atmosphere  is  2.00  X  icr4.     Calculate  a 
the  degree  of  dissociation  for  930°  at  100  and  at  200  atmos- 
pheres.    2  NH3  =  N2  +  3  iH2 

Ans.    a  =  0.9875  at  100  atmos. 
a  =  °-9753  at  200  atmos. 

VIII.  In  the  formation  of  SO3  according  to  the  equilib- 


rium equation  SO2  +  \  O2  ^  SO3,  calculate  the  ratio 


S03 
SO2 

if  the  partial  pressures  of  the  oxygen  in  the  initial  mixture  of 
SO2  and  O%  are  respectively  0.25,  0.50,  i\oo,  2.00,  and  3.00 
atmospheres. 


=  100 


QO 

Assume  — -  =  x  and  solve. 

SO2 
Ans.     50,  70.7,  100,  141,  173. 


520 


PHYSICAL   CHEMISTRY 


IX.   The  following  are  the  values  of  KP= 


from 


Bodenstein's  measurements  for  the  reaction 

SO3  ^  SO2  +  \  O2.     Calculate  the  degree  of  dissociation, 
«,  for  the  values  of  KP. 


TEMP. 

KP 

Ans.  a 

528 

31-3 

O.II9 

579 

13-8 

0.192 

627 

5-54 

0.313 

680 

3-24 

0.403 

727 

1.86 

0.516 

789 

0.956 

0.653 

832 

0.627 

0.713 

897 

0.358 

0.807 

In  order  to  calculate  the  degree  of  dissociation,  first  assume 
values  of  a  and  calculate  KP.  Now  plot  these  values  of  a 
against  KP  on  a  very  large  scale  about  two  by  three  feet. 
From  the  curve  obtain  the  values  of  a  which  correspond  to 
the  given  values  of  KP  at  the  designated  temperature.  The 
following  table  illustrates  the  assumed  values  of  a  which  may 
be  selected  with  the  corresponding  value  of  KP : 


ASSUMED  VALUES 

OF  a 

KP 

ASSUMED  VALUES 

OF  a 

KP 

.1 

40.26 

•5 

2.OO 

.12 

29-95 

.6 

1.22 

•15 

20.68 

•7 

0.723 

.2 

12.65 

.8 

0-395 

•3 

6.03 

•9 

0.166 

4 

3.36 

APPENDIX  521 

TABLE  XII 
Surface  Tension  and  Association  Factors 


1.  By  employing  the  equation  y  =    •—  the  value  for  any 

one  term  may  be  calculated,  providing  the  others  are  known. 
The  values  of  these  terms  are  given  in  Table  XIII,  from 
which  calculate  y. 

2.  The   constant   of    the   equation    y(mV)%  =  k\(r  —  d) 
(where  r  =  tt  —  t,  d  =  6)  is  required  in  order  to  calculate 

the  association  factor  x  (from  the  equation  x 


and  k\j  which  has  a  value  of  2.12  for  normal  liquids,  is  ob- 
tained by  solving  two  simultaneous  equations  for  different 
temperatures.  In  the  table  are  given  the  data  at  a  number 
of  different  temperatures,  from  which  calculate  the  value 
for  ki,  then  calculate  the  association  factor. 

Tate's  Law  is  y  =  kw,  in  which  w  is  the  weight  of  a  drop 
of  the  liquid  and  k  is  a  constant  for  a  given  tip  of  the  capillary 
tube  from  which  the  liquid  drops.  In  calculating  the  asso- 
ciation factor  from  the  falling  drop  data,  the  same  general 
formula  as  was  used  above  is  employed  ;  but  instead  of  2 . 1 2 , 
the  constant  for  normal  liquids,  the  constant  kw,  obtained 
from  the  following  relation,  must  be  employed,  y  :  w : :  2.12  :  kw. 

Solving,  we  have  kv  =  2'12  w .  Calculate  the  association  fac- 
tor, using  the  weight  of  the  drop. 

3 .  The  capillary  constant  or  the  specific  cohesion  is  repre- 
sented by  a2,  and  by  definition  we  have  a2  =  rh.  From  the 

equation  y  =  &LB.t  we  then  have,  since  g  =  981,  y  =  9  r  ap, 

and  when  a2  is  expressed  in  millimeters  we  have  y  =    ap  , 

0.204* 


522 


PHYSICAL  CHEMISTRY 


or  a2  =  — — 4_2.     Calculate  the  values  for  a2  from  the  data 

p 
in  the  accompanying  table. 


TABLE  XIII 

Relation  of  Latent  Heat  of  Vaporization  and  a?,  and 
Trouton's  Law 


SUBSTANCE 

P 

/ 

WEIGHT 
or  DROP 

MG. 

y 

h 

CM. 

r 

CM. 

ASSOCIA- 
TION CON- 
STANT 

a 

a* 
MM? 

i.   Acetone       .     .     . 

0.80177 

i5-o° 

25.674 

23-49 

3-IOO 

0.0193 

5-99 

B.  Pt.       56.5° 

0.78348 

30.1 

23.610 

21.64 

2.917 

1-34 

563 

LV          125.3  cal. 

0.74962 

60.0 

19.642 

17.97 

2-539 

1.24 

4.90 

2.   Acetonitrile      .     . 

0.7929 

10 

32.545 

29.50 

4.120 

0.01843 

T    78 

7.6 

B.  Pt.        80.5° 

0.7607 

40 

28.385 

25-73 

3-741 

I.7O 

6.9 

LV           173.6  cal. 

0.7500 

50 

27.015 

24.50 

3.6l8 

1.97 

6.67 

3.   Benzaldehyde 

B.  Pt.      179-9° 

1-0349 

30.2 

42.358 

37-42 

4-843 

O.OI522 

7-38 

Lv             86.6  cal. 

1.0169 

50.0 

39-9I4 

35-27 

4-650 

1.22 

7.08 

4.   Benzene       .     .     . 

0.8043 

90 

21.40 

19-225 

3-772 

O.OI294 

O.9O 

4-88 

B.  Pt.        80.3° 

0.8171 

78 

23.06 

20.75 

2.810 

0.01843 

I.OO 

5-i8 

Lv             93-5  cal. 

0.8565 

4i 

28.08 

25.27 

3.122 

0.0193 

6.026 

5.   Hexane       .     .     . 

B.  Pt.        70.0° 

0.67795 

o.o 

22.404 

20.7 

3-995 

O.OI56 

_    Qr\ 

6.232 

Lv            79-4 

0.65213 

30.0 

19.152 

17-5 

3-490 

0.09 

5-449 

6.   Prophyl  alcohol    . 

0.8035 

20 

26.046 

23.01 

4.108 

O.OI425 

5-85 

B.  Pt.        97-3° 

0.7875 

40 

24.274 

21.45 

3.919 

2-35 

5-58 

LV          166.3  cal. 

0.7700 

60 

22.503 

19.88 

3.688 

2.40 

5-26 

7.   Water     .... 

0.99987 

0.0 

84-325 

75-87 

I2.OO 

O.OI29 

2.88 

15-49 

B.  Pt.      100° 

0.99913 

15-0 

81.643 

73-50 

11.62 

0.0129 

-    Q, 

15-03 

Lv           53  5-8  cal. 

0.99567 

30.0 

78.940 

71.03 

II.  2Q 

0.0129 

2.ol 
«  OT 

14-57 

0.98324 

60.0 

73.148 

65.80 

9-58 

O.OI425 

2.ol 

2  68 

13-65 

0.97781 

70.0 

71.068 

63-97 

9-37 

O.OI425 

13-34 

Walden  showed  that  the  latent  heat  of  vaporization,  Lv, 


divided  by  a2,  is  a  constant,  i.e.  -~  =  17.9. 


In  the  table 


the  necessary  data  are  given  so  that  the  constant  can  be  cal- 
culated, or  either  of  the  values  may  be  calculated  by  assuming 
the  others  known.  It  will  be  observed  that  the  values  in 
this  table  are  not  the  constant  value  17.9,  but  if  the  value 
found  from  the  latent  heat  of  vaporization  and  a2  be  divided 


APPENDIX 


523 


by  the  constant,  the  result  is  a  value  that  approximates  very 
closely  to  that  given  for  the  association  factor  in  the  last 


SUBSTANCE 

BOILING 
POINT 

LV 
CAL. 

a? 

Lv 
<£>• 

mLy 

~TV 

ASSOCIATION 
FACTOR 

LV    _ 

(T>'-« 

17.9  <*~ 

i  .   Carbon        tetra- 

chloride       .     . 

76.2° 

46.4 

2.59 

17.9 

20.4 

I.OO 

1.  01 

2.  Carbon  bisulphide 

46.2 

86.67 

4.90 

177 

20.  6 

0.99 

1.07 

3.    Chloroform     .     . 

60.9 

58.4 

3.20 

18.2 

20.8 

I.  O2 

1.03 

4.   Ether    .... 

34-8 

84-5 

4.72 

17.9 

20.4 

I.OO 

0.99 

5.    Ethyl  iodide   .     . 

71-3 

46.0 

2.58 

17.8 

2O.8 

0.99 

0.96 

6.   Phosphorus   chlo- 

ride   .... 

78-5 

51.42 

2.67 

19.2 

20.1 

1.07 

.02 

7.    Acetone      .     ,  '; 

56.6 

125-38 

5.00 

25.2 

22.1 

1.41 

.26 

8.   Acetonitrile    . 

81.5 

170.6 

5-93 

29.4 

20.4 

1.64 

.67 

9.   Allyl  alcohol 

96.5 

163-3 

4.88 

33-5 

25-6 

1.87 

.86 

10.   Aniline 

183.0 

II3-9 

5-73 

19.9 

20.8 

I.  II 

.05 

ii.   Chlorbenzene 

130.0 

74.24 

4.02 

18.4 

20.7 

1.  08 

.03 

12.    Ethyl  alcohol 

78.2 

216.5 

4-74 

45-8 

28.4 

2.56 

243 

13.    Methyl  alcohol   . 

60.0 

269.4 

4-33 

61.7 

254 

345 

343 

14.    Methyl         ethyl 

ketone    ...-*•     . 

79-5 

103.8 

4-65 

22.3 

21.2 

1.24 

I-I5 

15.   Methyl       propyl 

ketone    .     .     . 

94.0 

88.7 

4.63 

19.2 

20.8 

1.07 

i.  06 

1  6.    Nitrobenzene 

151-5 

79.2 

5.32 

14.9 

23.0 

0.83 

I-I3 

17.    Propionitrile 

C2H5CN       .     . 

97.2 

1344 

5-24 

257 

2O.O 

143 

1-57 

1  8.   Propyl  alcohol 

97-3 

166.3 

4.66 

35-7 

27.0 

1.98 

2.40 

19.   Water  .... 

IOO.O 

535-8 

12.41 

43-2 

25-9 

2.41 

2.68 

column.     So  the  values  for  the  association  factor  obtained 

from  the  formula  -  — 
17.9  a2 

column. 


x  are  given  in  the  next  to  the  last 


Trouton's  Law  is 


20.6,  in  which  m  is  the  molecular 


weight;    Lv,  the  latent  heat  of  vaporization;    and  Tv,  the. 


524 


PHYSICAL  CHEMISTRY 


temperature  on  the  Absolute  scale  at  which  the  heat  of 
vaporization  was  determined.  The  boiling  point  under 
760  mm.  pressure  is  usually  given  in  the  formula.  The 
value  of  the  constant  can  be  calculated  if  the  other  values 
are  given,  or  assuming  all  values  known  but  one,  this  may 
be  calculated. 

TABLE  XIV 
Construction  of  Temperature-Concentration  Diagrams 

From  the  data  for  each  of  the  following  systems,  plot  the 
liquidus  and  solidus  curves  on  a  temperature-concentration 
diagram,  and  draw  the  horizontals  at  the  transition  points  and 
at  the  eutectic  points.  Indicate  the  solid  phase  separating 
along  each  liquidus  curve,  and  the  components  of  the  systems 
in  equilibrium  in  the  various  areas  into  which  the  curves 
divide  the  diagram. 


COMPOSI- 

SYSTEM 

MELTING 
POINTS 

TION 
WEIGHT 

SOLID  PHASE  SEPARATING 

PER  CENT  * 

I.   Mg  -  Bi   .     ..    / 

650.9° 

0 

Eutectic   composed   of   Mg 

552 

65 

—  Mg3Bi2 

715 

85 

Mg3Bi 

268 

IOO 

2.   Au  -  Sb    .     .     . 

1064 

0 

360 

25 

Eutectic  Au-AuSb2 

460 

55 

AuSb2 

631 

IOO 

3.   Bi  -  Te     .     .     . 

267 

o 

26l 

2 

Eutectic  Bi—  Bi2Te3 

573 

48 

Bi2Te3 

388 

85 

Eutectic  Bi2Te3-Te 

428 

IOO 

*  The  value  in  this  column  is  the  per  cent  of  the  member  of  the  system  named 
last. 


APPENDIX 


525 


COMPOSI- 

SYSTEM 

MELTING 
POINTS 

TION 
WEIGHT 

SOLID  PHASE  SEPARATING 

PER  CENT 

4.    Cu  -  Mg      .     . 

1084 

0 

730 

9 

EutecticCu-Cu2Mg 

797 

Cu2Mg 

555 

33 

Eutectic   Cu2Mg  —  CuMg2 

570 

CuMg2 

485 

68 

Eutectic     CuMg2  —  Mg 

650 

100 

5.    Si  -  Mg  .      .     . 

1408 

0 

950 

42.5 

Eutectic     Si-Mg2Si 

IIO2 

Mg2Si 

646 

96 

Eutectic  Mg2Si  —  Mg 

66  1 

IOO 

6.    NaNO3-KNO3 

308 

0 

Eutectic     consists     of     two 

218 

52 

solid  solutions  containing 

339 

IOO 

20    and    87    per    cent    of 

KNO3  respectively 

7.   Au  —  Sn       . 

1064 

0 

280 

20 

Eutectic:     solid   solution   5 

per  cent  Sn  —  AuSn 

440 

AuSn 

AuSn2  transition  point 

309 

252 

AuSiLi  transition  point 

217 

90 

Eutectic     AuSn4  —  pure  Sn 

232 

IOO 

8.   Au  -  Co      .     . 

1064 

0 

997 

IO 

Eutectic:     two    solid    solu- 

tions containing  5  and  97 

per  cent  of  Co  respectively 

1493 

IOO 

PHYSICAL   CHEMISTRY 


COMPOSI- 

SYSTEM 

MELTING 
POINTS 

TION 
WEIGHT 

SOLID  PHASE  SEPARATING 

PER  CENT 

9.   Li2SiO3—  BaSiO3 

1169 

o 

Eutectic      consists    of    two 

880 

58 

solid  solutions  containing 

1490 

IOO 

1  6    and    84   per    cent    of 

BaSiO3  respectively 

10.   PbF2  -  PbCl2 

824 

o 

570 

4  PbF2  •  PbCl2-  transition 

point 

554 

24 

Eutectic  :   4  PbF2  •  PbCl2 

and    solid    solution    con- 

taining 42  per  cent  PbCla 

601 

•  PbF2  •  PbCl2 

454 

90 

Eutectic  :      solid     solutions 

containing  53  per  cent  and 

495 

IOO 

97  per  cent  PbCl2  respec- 

tively 

TABLE  XV 
Index  of  Refraction 

From  the  data  in  the  following  table  calculate  the  molec- 
ular refractivity  by  the  Gladstone- Dale  formula  and  also 
by  the  n2  formula,  from  which  the  values  given  in  the  table 
were  obtained. 

Then  compare  these  values  with  those  obtained  by  calcu- 
lating the  molecular  refractivity  by  employing  the  atomic 
refractivities  given  in  Table  XIX,  page  127. 

Given  the  experimental  value  for  the  index  of  refraction, 
n,  for  toluene  and  the  atomic  refractivities,  calculate  the 
number  of  double  bonds. 

Similarly,  the  structural  relation  of  compounds  containing 
oxygen  may  be  ascertained  by  determining  whether  the  oxygen 
has  the  value  for  carbonyl  oxygen,  hydroxyl  oxygen,  etc.,  and 
from  this  determine  whether  the  compound  is  a  ketone,  alcohol, 
etc.  Or,  assuming  the  value  for  one  element  to  be  unknown, 
calculate  its  atomic  refractivity  from  the  other  known  values. 


APPENDIX 


527 


The  molecular  refractivity  for  either  the  D  line  or  for  the 
hydrogen  line  may  be  calculated.  By  calculating  both  of 
these  values  the  molecular  dispersion  may  be  obtained. 


P4o 

rt 

LINE 

TEMP. 

MOLECU- 
LAR RE- 
TRACTION 

i.   Cymene 

0.8619 

1.4926 

D 

IT.  7 

45.18 

CH3-  C6H5-  CH(CH3)2    . 

1.5111 

HT 

o  / 

46.62 

2.   Naphthalene       .... 

0.9621 

1.58232 

D 

98.4 

4446 

XCioH8    .... 

1.57456 

Ha 

43-97 

j 

3.   Toluene     

0.8707 

1  .4QQ2 

D 

14.7 

06 

C8H5  •  CH3 

\J  .w  j  \J  j 

M.    .L^.  J  J*. 

Ha 

Atf..  j 

30.80 

4.   Acetophenone     .... 

1.0293 

L53427 

D 

I9.I 

36.28 

C«H6  -  CO  •  CH3     .     .     . 

L52837 

Ha 

• 

35-95 

5.   Benzaldehyde     .... 

1.0455 

1.54638 

D 

2O 

32.15 

C6H6  •  CO  •  H    .     .     .     . 

1-57749 

HT 

33-64 

6.   Methyl  ethyl  ketone    .     . 

0.8087 

1.38071 

D 

15.9 

20.67 

CH3  -  CO  •  C2H6     .    .     . 

1.37844 

Ha 

20.56 

7.   w-Butyric  acid    .... 

0.9587 

1.39789 

D 

2O 

22.16 

CH3  •  CH2  •  CH2  •  COOH 

8.  i-Btttyric  acid     .... 

0.9490 

1.39300 

D 

2O 

22.15 

/-ATT     /  CH  •  COOH    . 

V^±13  / 

9.   Ethyl  acetate      .... 

0.9007 

1.37257 

D 

2O 

22.25 

CH3COOC2H6    .     ... 

10.   Methyl  propionate      .     . 

0.9166 

1.37767 

D 

I8.5 

22.13 

CH3  •  CH2  •  COOCH3  .     . 

1  1  .   Benzal  alcohol    .... 

1.0456 

1.53938 

D 

22.1 

32.41 

C«H6  •  CH2  -OH     ... 

12.   w-Butyl  alcohol  .... 

0.8099 

1.39909 

D 

2O 

22.13 

CH3  •  CH2  •  CH2  •  CH2  • 

OH  

13.   Ethyl  alcohol      .... 

0.8000 

1.36232 

D 

20 

12.78 

C2H5  •  OH      

i.  ^6007 

HY 

1^.02 

14.   Ethyl  trichloracetate  . 

1.3826 

O      s  s  i 

1.45068 

D 

2O 

J.  ^}»V^ 

37-25 

CC13COOC2H5    .... 

i  .44802 

Ha 

37.06 

15.   Propargyl  alcohol   .     .     . 

0.9715 

1.43064 

D 

2O 

14.92 

CH  i  C  •  CH2  -OH      .    .. 

1.44277 

HT 

15.28 

1  6.    w-Propyl  alcohol      .     .     . 

0.8044 

1.38543 

D 

2O 

17.52 

CH3-  CH2-CH2-OH.     . 

1-39378 

HT 

17.85 

528 


PHYSICAL   CHEMISTRY 


TABLE  XVI 
Calculation  of  Osmotic  Pressure 

Calculate  the  osmotic  pressure  from  the  data  given  in  the 
following  table.  Or,  assuming  the  osmotic  pressure  known, 
calculate  the  apparent  molecular  weight,  mA,  and  then  the 
degree  of  dissociation,  a. 

For  additional  problems  see  tables  of  data,  page  534. 


SOLVENT 

SOLUTE 

CONCENTRATION 

PO  IN 

ATMOS. 

a 

^ 

grams  in 

H20        .     . 

Cane  sugar 

1000  cc.  solution 

i  =  o°   .'    . 

Ci2H22On 

2.  02 

0.134 

337-5 

20. 

1.32 

339- 

93-75 

6.18 

339-5 

300. 

26.8 

250.4 

750. 

134.7 

124-5 

n  in  80  liters 

H2O       .     . 

K2S04 

5-0 

2.82 

449 

91.9 

t  =  17°.     . 

4.0 

2.19 

415 

94-7 

3-o 

1.705 

456 

91-3 

2.O 

1.  01 

•35 

102.4 

1.0 

0.66 

.610 

78-5 

n  in  160  liters 

H20       .     . 

KtFeCNs 

8.0 

344 

473 

127-5 

t  =  17°  .     . 

4.0 

1.92 

•5565 

114.1 

2-5 

1.27 

.6045 

107.9 

2.0 

0-95 

•549 

1154 

I.O 

0.50 

•591 

109.4 

i  mole  in  20  liters 

H2O  .     .     . 

KN03 

1.68 

.414 

71-5 

t  =  17°.     . 

NaNO3 

1.79 

-5i 

56.5 

NH4NO3 

1.48 

•245 

64-3 

Mg(N03)2 

2.12 

-391 

83-3 

Ca(N03)2 

1.67 

.202 

116.9 

Sr(N03)2 

1.58 

.165 

158.9 

Ba(N03)2 

2.04 

•359 

152.0 

APPENDIX 


529 


TABLE  XVII 

Osmotic    Pressure,  —  Comparison    of    Normal    Weight    and 
Normal  Volume  Concentrations 

Check  the  values  for  p0  in  the  following  table  by  interpo- 
lation from  density  tables  of  sugar  solutions  such  as  given  in 
Landolt  and  Borns tern's  Tabellen.  Then  express  the  con- 
centration in  moles  per  liter  (molal  volume  concentration) 
and  in  moles  per  1000  grams  of  solvent  (molal  weight  concen- 
tration) .  Calculate  the  osmotic  pressure,  using  each  of  these 
values  for  the  concentration  and  ascertaining  which  set  of 
results  conforms  more  nearly  to  the  observed  values. 


OSMOTIC  PRESSURE  IN  ATMOSPHERES 

GRAMS  IN 
i  LITER 

PO 

Observed 

CALCULATED  VALUES 

SOLUTION 

Assuming 

Berkeley  & 

Cone.  Molal 

Po 

Cone.  Molal 

Po 

both  Asso- 

Hartley's 

Volume  n 

in  Atmos. 

Weight  n 

in  Atmos. 

ciation 

Hydration 

IO.O 

.0000 

0.66 

O.O2922 

0.654 

0.02952 

0.661 

0.663 

45-o 

.0180 

2.97 

O.I3I5 

2.94 

0.1354 

3-025 

3-07 

150.8 

•0597 

II.80 

0.4405 

9.86 

0.4847 

10.85 

II.4 

1  80.  i 

.0713 

13-95 

0.5262 

n.8 

0.5904 

13.22 

14.0 

420.3 

.1634 

43-97 

1.228 

27-5 

1.652 

37-0 

43-7 

540-4 

1.2086 

67-5I 

1-579 

35-35 

2.364 

52.9 

68.0 

The  data  in  this  table  may  also  be  employed  in  the  calcu- 
lation of  the  osmotic  pressure  by  the  modified  formula  (page 
363)  wherein  correction  is  made  for  association  of  the  solvent 
and  hydration  of  the  solute.  On  the  basis  that  the  associa- 
tion factor  of  water  is  x  =  1.65,  calculate  the  osmotic  pressure 
on  the  normal  weight  basis,  then  calculate  the  value  of  the 
osmotic  pressure,  assuming  the  hydration  is  Ci2H220n  •  6  H2O, 
and  then  calculate  the  osmotic  pressure,  assuming  both 
hydration  and  association.  The  values  are  given  in  the  last 
column  in  the  table. 


530 


PHYSICAL   CHEMISTRY 


TABLE  XVIII 
Vapor  Pressure  Calculations 

In  order  to  determine  the  molecular  weight  from  the  lower- 
ing of  the  vapor  pressure  Raoult's  modified  formula  for  the 
vapor  pressure  is  used  : 


Solving 

Since 

Since 


m 


i  =  — ,  solve  for  i. 
mA 


a  =  -?- ^- ,  solve  for  a. 


The  following  data  are  for  aqueous  solutions  wherein  100 
grams  of  the  solvent  were  employed  in  each  case.  The  vapor 
pressure  of  water  at  o°  C.  is  4.62. 


SOLUTE 

GRAMS 

VAPOR  PRES- 
SURE OF  SOLU- 
TION Pi 

mA 

Cane  sugar 

-I  Q7T 

A     (}I2 

AI2 

t  =  o°      

o-V/  x 

8  72 

4  600 

41^ 
^6  1 

1  7  11 

4C7Q 

1A8 

Urea       

1/-o1 
33.89 

68.2 
o  810 

•o/y 
4-533 
4-439 

4  61  1 

o4° 
318 
301 

7  A.  7 

CO(NH2)2 

i  614 

A  6O1 

78  7 

/  =  o°     .     .     .     . 

2  o6j. 

A  ^86 

71  O 

5.976 

I2.O 
24.0 
36.0 
60.0 

4-550 
4.485 
4.356 
4.212 
3.968 

69.9 
71.7 

71-5 
67.0 

657 

APPENDIX 


531 


VAPOR  I 

RESSURE 

SOLUTE 

1 

of  Solvent 
P 

of  Solution 
Pi 

a 

mA 

Sodium  chloride        .     . 

19.14 

16.61 

14.4 

•474 

23.6 

NaCl      

32.07 

35-88 

3I-I 

•483 

23-5 

g  =  20.08  gr.        ... 

41.24 

59-29 

51-3 

-5i8 

23-2 

50.00 

92.54 

79-6 

•625 

22.3 

59-99 

149.46 

129.7 

•465 

23-7 

69-37 

227.79 

196.7 

•555 

22.9 

79-50 

348.34 

300.3 

.583 

22.6 

89.72 

520.04 

449-7 

•533 

23.1 

95-12 

636.34 

5534 

423 

24.1 

Potassium  chloride  .     . 

14.2 

12.15 

1  1.  2 

•755 

42.5 

KC1        

2S6 

24.  6^ 

22.2 

.260 

T.'l  O 

g  =  20.04        .... 

^  O 

29.7 

•^'6r'v/O 

31.29 

28.4 

.100 

OO-" 

35.5 

40.5 

56.83 

51-3 

.236 

33-5 

49-7 

91.18 

83.1 

.010 

37-1 

60.9 

155-8 

140.7 

.220 

33-6 

68.9 

222.9 

201.  1 

.240 

33-3 

77.2 

317.0 

287.5 

.I2O 

35.2 

85-4 

440.6 

399-3 

.138 

34-9 

94-7 

627.0 

570.1 

.060 

36.2 

Calcium  chloride      .     . 

17-5 

15-0 

13-5 

.219 

32.38 

CaCl2               .... 

2Q  ^ 

T.Q  eg 

26  Q 

600 

26    ^1 

g  =  19-99    

*3r*O 

39-5 

O^'V 

53-88 

•^"•7 
47.1 

,\J\sy 

.720 

^V-'*O  J. 

25.00 

50.2 

93-47 

81.6 

-744 

24.74 

74.2 

279.8 

245-8 

.636 

25-99 

g  =  I5-IO   

20.3 

17.87 

16.2 

.605 

26.37 

31.2 

34-09 

30.9 

.608 

26.33 

44-i 

68.64 

62.6 

.469 

28.18 

56.8 

128.7 

117.2 

-504 

27.70 

72.0 

254.8 

232.2 

.487 

27-93 

TABLE  XIX 
Lowering  of  the  Freezing  Point  and  Rise  of  the  Boiling  Point 

Calculate  the  apparent  molecular  weight  of  the  solute  in 
water  from  the  following  data.     In  the  case  of  electrolytes, 


532 


PHYSICAL  CHEMISTRY 


calculate  the  degree  of  dissociation.  Assuming  the  formula 
weight,  m,  calculate  the  apparent  molecular  lowering,  KA, 
or  the  apparent  molecular  rise.  For  additional  problems  see 
tables  of  data,  page  534. 


SOLUTE 

GRAMS  IN  100 
GRAMS  OF 
WATER 

LOWERING  OF 

rREEZING  POINT 
A 

CALCULATED  VALUES 

K  =  18.6 

m 

»4 

a 

KA 

Cane  sugar      .     . 

0.04825 

O.O0264 

340. 

18.7 

CizHzzOn     • 

0.6878 

0.0378 

338.3 

1  8.  8 

9.778 

0.5387 

336. 

18.9 

26.008 

1.466 

330. 

19-3 

29.82 

1.768 

3H- 

20.3 

34.20 

2.07 

307. 

20.7 

Acetone       .     .     . 

0.1191 

0.0372 

59-6 

18.12 

(CH3)2CO   .     .     . 

0.5851 

0.1846 

59-0 

18.3 

3.007 

0.920 

60.8 

17.8 

6.221 

1  .930 

60.0 

18.0 

22.19 

6-55 

63.0 

17.2 

45-30 

12-35 

68.2 

15-8 

NaCl      .... 

O.OIO47 

O.O06403 

304 

.922 

35-8 

0.03738 

0.02339 

29.8 

.960 

36.6 

0.1250 

0.07584 

30.7 

.903 

354 

0.690 

0.4077 

31-5 

•855 

34-6 

3-099 

1-759 

32.8 

.780 

33-2 

5-770 

3-293 

32-6 

.792 

33-4 

NaNO3  .... 

O.I97O 

0.0817 

44.8 

.896 

35-2 

0.5224 

O.2I24 

45-7 

.858 

34-6 

1.620 

0.6318 

47-7 

.781 

33-2 

4.328 

I.62I 

49.6 

.712 

31-9 

8.526 

3.040 

52.2 

.628 

30-3 

KC1  

O.OOI92 

O.OOO953 

37-47 

.991 

^7.02 

0.07632 

0.03674 

O  /     T^/ 

38.63 

-7-7 

•931 

O  I 

35-92 

I.I23 

0.5140 

40.64 

•835 

34-14 

2.526 

I.I3II 

41-54 

•795 

33-41 

7.46 

3.2864 

42.22 

.767 

32.86 

APPENDIX 


533 


. 

CALCULATED  VALUES 

SOLVENT 

SOLUTE 

GRAMS  IN  100 
GRAMS  OF 
WATER 

RISE  OF 
BOILING 
POINT 

A 

£=5.2 

m  = 

mA 

a 

*A 

H2O 

NaCl 

0.4388 

0.074 

30.8 

-895 

9.86 

K  =  5.2 

2.158 

0.351 

31-9 

.830 

9-52 

mF  =  58.45 

7.27 

1-235 

30.6 

.908 

9.92 

12.17 

2.182 

29.0 

I.OI2 

10.48 

18.77 

2.866 

25.2 

I.3I7 

12.04 

H2O 

KNO3 

0.505 

0.051 

51-5 

.965 

10.21 

#   =  5.2 

2.789 

0.248 

58.5 

.730 

9.0O 

mp  =  101.1 

9.22 

0-797 

60.2 

.681 

8.76 

35-54 

2.710 

68.2 

.484 

7-72 

53-37 

3-795 

73-2 

-382 

7.21 

H2O 

CaCl2 

0.585 

0.091 

334 

I.I62 

17.26 

#  =  5-2 

2.405 

0.302 

41.4 

.841 

13-95 

mp  =m. 

5-35 

0.643 

43-2 

•782. 

13-34 

10.89 

1.481 

38-2 

•953 

I5-H 

TABLE  XX 
Electrical  Conductance 

From  the  data  in  the  following  tables  calculate  the  degree 
of  electrolytic  dissociation,  the  osmotic  pressure,  the  freez- 
ing point,  and  the  vapor  pressure  of  the  solution. 

TABLE  A 


SPECIFIC 
CONDUCT- 

TEMP. 

MOLES 
LITER 

ELECTRO- 

IONIC CONDUCTANCE 

DEGREE  OF 
DISSOCIATION 

ANCE 

n 

LYTE 

a  PER  CENT 

K 

i.  .2586 

1  8° 

2.924 

NH4C1 

NH4  =    64.7           Cl  =  65.5 

67.9 

2.     .1231 

18 

2.168 

SrCk 

*  Sr  =    51.9           Cl  =  65.5 

24.2 

3.     .0296 

18 

0.387 

Lil 

Li  =    33.3              I  =  66.6 

76.7 

4-    -1303 

18 

2.688 

NaNOa 

Na  =    43.4        NOa  =  61.8 

46.1 

5-    -0718 

18 

1.  000 

K2SO4 

K  =    64.5      i  SO4  =  68.5 

27.0 

6.    .1061 

18 

8.052 

MgCk 

*Mg  =    45.9            Cl  =  65.5 

5-Qi 

7.    .0508 

18 

0.790 

(COOH)2 

H  =  3I4-S     i  Cj04  =  63. 

8.52 

534 


PHYSICAL  CHEMISTRY 
TABLE  B 


EQUIVALENT 
CONDUCT- 
ANCE 

TEM- 
PERA- 
TURE 

VOL- 
UME 
LITERS 

EQUIVALENT 
CONDUCTANCE 

AOQ 

ELECTROLYTE 

DEGREE  OF 
DISSOCIATION 

a 

OSMOTIC 
PRES. 
ATMOSPHERES 

Ap 

V 

i.    18.1 

18° 

O.I 

133.0 

KzCOs 

.136 

153-7 

2.   42.7 

18 

0.2 

109.0 

NaCl 

•392 

166.2 

3-    53-i 

18 

0-5 

98.9 

LiCl 

•537 

73-3 

4.   46.0 

18 

0-33 

105.33 

NaNOa 

•437 

102.8 

5-    28.9 

18 

I.O 

109.9 

MgSO< 

.263 

15.08 

6.   70.0 

18 

O.I 

368.0 

H2S04 

.190 

164.8 

7-     21-5 

18 

O.2 

111.9 

Ca(NOs)2 

.192 

82.6 

8.   38.4 

18 

0-S 

111.7 

Sr(NOs)2 

•344 

40.25 

9-    26.3 

18 

I.O 

82.3 

Ca(C2H3O2)2 

-320 

19-55 

10.   42.2 

18 

0.2S 

118.7 

SrCk 

.356 

81.7 

it.    56.6 

18 

2. 

"5-3 

Ba(NO3)2 

.491 

11.82 

TABLE  C 


SPECIFIC 
CONDUCT- 
ANCE 

K 

TEMP. 

CONC. 
PER 
CENT 

DEN- 
SITY 
GRAMS 

PER  CC. 

AOO 

ELECTRO- 
LYTE 

DEGREE 
OF  DIS- 
SOCIATION 
PER  CENT 

FREEZING 
POINT 

VAPOR 
PRES- 
SURE 

MM. 

p 

a 

I.     .3948 

1  8° 

5 

1.0242 

376 

HC1 

74-8 

-4.70 

14.70 

2.     .1211 

18 

10 

1.0707 

109 

NaCl 

60.6 

-5-68 

14-59 

3-    -0389 

18 

5 

1.0445 

117 

BaCh 

66.0 

-  1.09 

15-21 

4.     .1728 

18 

20 

-1794 

II5-2 

CaClz 

35-22 

—  7.14 

14.38 

5-    -0469 

18 

50 

.5102 

112 

Ca(NOs)2 

15.2 

—  14.80 

13-45 

6.    .0458 

18 

5 

•0395 

130.7 

K2S04 

50.2 

-  i.  125 

15-22 

7-    -1505 

18 

20 

•133 

126.5 

KNOs 

53-0 

—  7-04 

14-39 

8.    .0651 

18 

2O 

.104 

76.4 

NaC2H302 

31.62 

-7.46 

14-33 

9.   .001081 

18 

40 

1.0496 

IO7.O 

CHsCOOH 

0.145 

-  23.66 

12.50 

10.   .0783 

18 

7 

1.0326 

235-2 

(COOH)2 

20.7 

—   2.20 

15-08 

(Vapor  Pressure  of  water  at  18°  is  15.383  mm.) 

TABLE  XXI 
Ionic  Product 

The  calculation  of  the  solubility  of  difficultly  soluble 
substances,  either  alone  or  in  the  presence  of  a  more  soluble 
salt  containing  a  common  ion,  introduces  a  number  of  cases 


APPENDIX  535 

depending  upon  the  assumptions  made.  Two  of  the  simple 
cases  may  be  illustrated  by  a  consideration  of  uni-univalent 
or  bi-bivalent  and  of  uni-bivalent  salts  as  PbSO4  and  PbCl2. 

1.  PbSO4  ^  [Pb++]  +  [SO4~  ]  then  from  the  Law  of  Mass 
Action  [Pb++]  •  [SO4~]  =  L0.     But  the  concentration  of  the 
[Pb++]  =  the  concentration  of  the  [SO4~]  =  VZo  or  [Pb++]2 
=  L0.     Now  assume  that  a  definite  concentration,   c,    of 
(NH4)2SO4  is  added  to  a  specified  quantity  of  the  saturated 
solution  of  PbSO4.     What  will  be  the  concentration  of  the 
Pb++  present  ?     We  would  then  have  [Pb++]  •  [SO4—  +  c] 
=  LQ  ;  but  [Pb++]  =  [S04~~]  in  concentration,  hence 

[SO4~]  •  [SO4-  +  c]  =  L0  or  [SO4-]2  +  c[SO4-]  =  L0 
or  [S04-]2  +  c[S04-]  -  Lo  =  o. 

Solving  this  quadratic  equation  for  [SO4~~]  gives  the  ionic 
concentration  from  which  the  solubility  of  PbSO4  is  readily 
obtained. 

2.  PbI2:£  [Pb++]  +  [2  I-]    and  then    [Pb++]  •  [I~]2  =  L0. 
But  there  are  twice  as  many  [I~]  as   [Pb++],  hence  [I~]  = 
[2  Pb++].     Then  [Pb++]  •  [2  Pb++]2  =  L0  or  4  [Pb++]3  =  L0  or 


[Pb++l  =  and   [I-]  =     17,  from  which  the  solubility 

4 
of  the  PbI2  can  be  calculated  or  the  concentration  of  the 

individual  ions.  Now  if  an  electrolyte  with  a  common  ion 
is  added  to  a  saturated  solution  a  cubical  equation  is 
obtained.  Show  the  form  of  this  expression  and  how  it 
may  be  employed  in  determining  the  solubility  of  the  diffi- 
cultly soluble  salt.  It  must  be  remembered  in  solving  the 
cubical  equation  that  since  the  root  is  a  very  small  decimal 
the  terms  involving  the  second  and  the  third  powers  are 
practically  negligible  with  respect  to  the  first  power,  hence 
a  very  close  approximation  may  be  obtained  by  employing 
the  term  involving  the  first  or  the  second  power  and  solving. 
This  method  of  approximation  was  utilized  to  obtain  the 
values  in  the  last  column. 


536 


PHYSICAL   CHEMISTRY 


From  the  data  presented  in  the  table,  calculate  the  Ionic 
Product.  This  is  obtained  by  expressing  the  concentra- 
tion of  the  ions  in  terms  of  gram-ions  per  liter  and  the  solu- 
bility obtained  from  these  values  would  be  expressed  in 
gram-molecules  or  moles  per  liter. 

To  100  cc.  of  a  saturated  solution  of  the  substance  listed 
in  the  first  column  add  100  cc.  of  the  designated  solution 
of  an  electrolyte  containing  a  common  ion.  This  substance 
is  assumed  to  be  completely  dissociated,  and  the  solution 
of  the  original  substance  is  to  remain  saturated.  Calculate 
the  concentration  of  the  original  substance  and  express  the 
same  in  moles  per  liter. 


CONCENTRA- 

SUBSTANCE 

1 

SOLUBILITY 

IONIC 
PRODUCT 

SUBSTANCE  ADDED 
CONCENTRATION 

TION  MOLES 
PER  LITER 
ORIGINAL 

SUBSTANCE 

i.  Ag2C03  .    .    . 

25 

3.2X10-'  per  cent 

6.25X10-!* 

Na2CO3     1.5  gr. 

4.70X10-* 

2.    AgjC2O4         .       . 

18 

1.2X10-*     moles 

6.9  Xio-« 

(NH4)2C2O4  •  H2O    sgr. 

3.13X10-* 

per  liter 

3.  Ag2CrO4      .     . 

25 

2.oXio"spercent 

0.9  Xio-« 

AgNOs    o.iN 

3-5  Xio-1" 

4.  BaCrO4  .     .     . 

18 

3.  5  Xio"4  per  cent 

1.9  X  io-"> 

K2CrO4     0.5  N 

3.8  Xio-i" 

5.  BaC*04  -  2  H20 

18 

0.0086  gr.  per  100 

1.44X10-' 

(NH4)2C204  •  H20  o.6N 

0.96X10-6 

g-H20 

6.  BaS04    .     .     . 

25 

2.  3  Xio-4  per  cent 

o.97Xio-"> 

(NH4)2SO4    0.2  N 

1.94X10-* 

7.  CaCsO4  .     .    . 

18 

4-35  Xio~6   moles 

1.89X10-* 

(NH4)2C2O4  •  H2O  0.5  N 

3.88Xio-» 

per  liter 

8.  Pblj  .... 

25 

i.  65X10-3   moles 

1.80X10-8 

Nal     i2.ogr. 

i.iaXio"7 

per  liter 

9.  Pb(I03)t     .     . 

25 

i.9Xio-3  gr.  per 

1.59X10-" 

Pb(NOj)2     10  gr. 

5.13X10-* 

100  gr.  H2O 

-M 

10.  SrSO4     .     .     . 

18 

i.  14X10-*  gr.  per 

0.37X10-* 

(NH4)2SO4     3-3  gr. 

2.96X10-* 

loo  gr.  H2O 

ii.  TIBr  .... 

25 

5.7X10-*  gr.  per 

4.0  Xio^ 

NaBr    4.53  gr. 

i.SoXio-5 

100  gr.  H2O 

APPENDIX 
TABLE  XXII 


537 


Ionic  Product,  Solubility  and  Specific  Conductance 

From  the  data  in  the  following  table  and  the  equivalent 
ionic  conductances  given  in  Table  L,  page  320,  calculate  the 
solubility  in  moles  per  liter.  Assume  the  conductance  of 
the  water  to  be  i.2Xio~6  mhos  in  all  cases.  Calculate  the 
ionic  product.  Or  assuming  the  solubility  calculate  the 
specific  conductance  of  the  solution. 


SUBSTANCE 

TEMP. 

SPECIFIC  CON- 
DUCTANCE 

SOLUBILITY 
MOLES  PER  LITER 

IONIC  PRODUCT 
*o 

i.   AgCl    .     .     . 

18° 

2.4    XlO~6 

I.OO    XIO~5 

1.0  Xio~10 

2.   Ag2C2O4  .     . 

18 

2.55   Xio~5 

1.04  Xicr4 

4.5   Xio~12 

3.   BaC2O4    .     . 

16.3 

67.7    Xio-6 

2.925  Xicr4 

i.i   Xio~7 

4.   PbSO4      .     . 

18 

3.24X10-* 

1.57   Xio~4 

2.46X10-8 

5.   T1C1     .     .     . 

25 

1680       XlO-« 

1.105X10-2 

I.22XIO"4 

6.   T12S04      .     . 

20 

149.4  Xio~4 

0.53  Xio-1 

5.96XIO-4 

By  employing  the  data  in  Tables  LVI  and  LVII 
tional  problems  can  be  readily  formulated. 


TABLE  XXIII 
Degree  of  Dissociation  of  Water 

Prom  the  data  given  in  Tai>ie  LXIII  calculate  the  degree 
of  dissociation  of  water  at  each  of  the  given  temperatures. 

TABLE  XXIV 
Hydrolysis  Constant  and  Per  Cent  of  Hydrolysis 

Draw  a  curve  representing  the  change  of  the  Ionic  Product 
(Dissociation  Constant)  of  water  with  the  change  in  tem- 
perature. Making  the  proper  correction  for  the  temperature 
for  the  dissociation  constant  and  employing  the  data  given 


PHYSICAL   CHEMISTRY 


in  Table  LVI  calculate  the  hydrolytic  constant  for  the  sub- 
stances in  the  following  table  and  then  calculate  the  per 
cent  of  hydrolysis  at  the  specified  temperature. 


SUBSTANCE 

TEMP. 

VOL.  IN 
LITERS 

HYDROLYSIS 
CONSTANT  K^ 

PER  CENT 
HYDROLYSIS 

I.  Acetanilid  HC1     .     .     . 

40° 

IO 

0.78 

89.7 

2.  Acetamid  HC1     .     .     . 

25 

10 

3.36 

97.2 

3.  Aniline  acetate     .     .     . 

40 

39-32 

3-86 

66.2 

4.  Ammonium  acetate  .     . 

100 

40.13 

17-95  X  10  4 

4.06 

5.  Ammonium  chloride 

25 

32 

0.578  X  io-« 

0.013 

6.  Butyronitril     .     .     «     . 

25 

IO 

5-78 

96.7 

7    Urea  HC1                  .     . 

25 

IO 

O.60d 

88.  s 

8.  Potassium  cyanide    .     . 

42.5 

9.63 

0.5  X  io~4 

2.2 

TABLE  XXV 

Speed  of  Reaction;   Affinity  Constant 

In  the  transformation  of  ammonium  cyanate  into  urea 
a  decinormal  solution  was  employed.  Calculate  the  value 
of  the  affinity  constant  k  assuming  the  reaction  to  be  mono- 
molecular.  Calculate  the  per  cent  transformed  at  each 
reading  and  in  what  time  one  half  will  be  transformed  at 
each  temperature. 


25°    a  =  23.5 

64.5°    a  =  22.9 

80.1°    a  =  22.9 

inmin. 

X 

i 

/ 

inmin. 

X 

1 

/ 
in  rain. 

X 

i 

1325 
1970 

2725 
5640 

5-6 
7.0 
9.0 
13-3 

mean 

0.000236 
0.000214 
0.000228 
0.000231 

20 

37 
50 
65 
95 
150 

7.0 
10.3 

12.  1 

13-8 

16.0 
17.7 
mean 

O.O22O 
0.0221 
0.0224 
0.0233 
O.O244 
0.0227 

7 

17 

37 
57 
97 

9.0 

14.6 

17.9 
19.5 

20.9 

mean 

0.093 
0.103 
0.097 

O.IOI 

0.108 

0.000227 

O.IOO 

0.0228 

APPENDIX 


TABLE  XXVI 


539 


Table  of  Atomic  Weights 

The  values  given  in  this  Table  of  Atomic  Weights  are  the 
ones  that  have  been  used  in  the  problems. 


Aluminium    . 
Antimony 
Argon 

.     .     Al 
.     .     Sb 
A 

27.1 

120.2 

•7Q    Q 

Manganese    . 
Mercury  .     . 
M^olybdenum 

.     .     Mn 
•     •     Hg 
Mo 

55-0 
200.  6 
96  o 

Arsenic      .     . 
Barium      .     . 
Bismuth    . 
Boron 

.     .     As 
.     .     Ba 
.     .     Bi 
B 

75-o 

1374 
208.0 
no 

Neon   . 
Nickel      .     . 
Nitrogen  .     . 
Oxvsfen 

.     .     Ne 
.     .     Ni 
.     .     N 

o 

2O.2 

58-7 
I4.O 

16  o 

Bromine    .     . 
Cadmium 
Caesium     . 
Calcium    .     . 
Carbon      .     . 
Chlorine    . 
Chromium 
Cobalt 

.     .     Br 
.     .     Cd 
.     .     Cs 
.     .     Ca 
.     .     C 
.     .     Cl 
.     .     Cr 
Co 

79-9 
112.4 
132.8 
40.1 

I2.O 

35-5 
52.0 

CQ  O 

Palladium 
Phosphorus  . 
Platinum 
Potassium     . 
Selenium  . 
Silicon      .     . 
Silver  .     .     . 
Sodium 

.     .     Pd 
.     .     P 

.     .     Pt 
.     .     K 
.     .     Se 
.     .     Si 
•     •     Ag 
Na 

106.7 
31.0 
195-2 
39-i 
79.2 
28.3 
107.9 

21  O 

Copper      .     . 
Fluorine    . 
Gold 

.     .     Cu 
.     .     F 
Au 

63.6 

19.0 

107  2 

Strontium     . 
Sulphur    .     . 
Tellu  rium 

.     .     Sr 
.     .     S 
Te 

87.6 
32.0 
127  ^ 

Helium      .     . 
Hydrogen 

.     .     He 
.     .     H 

4.0 
I.O 

Thallium  .     . 
Tin      .     .     . 

.     .     Tl 
Sn 

2O4.O 

Il87 

Iodine 

I 

127  o 

Titanium 

Ti 

48  I 

Iron 

Fe 

SS  8 

Tungsten 

W 

184  o 

Krypton    .     . 
Lead     .     .     . 
Lithium     . 
Magnesium 

.     .     Kr 
.     .     Pb 
.     .     Li 
Mg 

82.9 
207.2 
7.0 

24  1 

Uranium  .     . 
Vanadium 
Xenon      .     ! 
Zinc     .     .     . 

.     .     U 
.     .     V 
.     .     Xe 
.     .     Zn 

238.2 
51.0 
130.2 

6s  4 

INDEX 


Absolute  zero,  51 
Absorption  coefficient, 

definition  of,  155 

table  of,  155 

Acceleration,  definition  of,  3 
Acid,  definition  of,  328 

relative  strength  of,  383 
Additive  properties,  331 
Adiabatic,  definition  of,  284 
Adsorption,  453 

by  charcoal,  454 

by  dyes,  456 

Adsorption  compounds,  454 
Affinity,  475,  476 
Allocolloids,  445 
Allotropes,  189 
Allotropy,  189 

types  of,  190 
Association  constant,  402 
Association  factor,  method  of  de- 
termining, 119 
Asymmetry,  136 
Atomic  heat,  413 

definition  of,  90 
Atomic  theory, 

Dalton's  statement  of,  38 

Lucretius'  statement  of,  37 
Atomic  volume,  113 
Atomic  volume  curve,  69 
Avidity,  355 
Avogadro's  Hypothesis,  17,  41 

deduction  of,  from  the  Kinetic 
Theory  of  Gases,  86 

Base,  definition  of,  328 

relative  strength  of,  353 
Basicity  of  organic  acids,  331 


Bimolecular  reactions,  484,  491 
Binary  Systems 

Cu-Ag,  241 

Cu-Zn,  248 

Hg-Cd,  239 

Iron  Carbon,  250 

KCl-AgCl,  210 

K2CO3-Na2CO2,  212 

K2SO4-MgSO4,  243 

Li2SiO3-MgSiO3,  242 

Mg-Sn,  244 

MgSiO3-MnSiO3,  241 

Pb-Sb,  211 
Birotation,  142 
Boiling  point 

constants,  table  of,  299 

curves,  types  of,   175,  176,  178, 
179 

equation,  298 

of  concentrated  solutions,  374 

of  solutions,  273 
Boyle's  Law,  19 

deduction  of,  from  the  Kinetic 
Theory  of  Gases,  85 

deviation  from,  46 
Brownian  movement,  465 

Calorie,  definition  of,  412 
Calorific  power 

of  foods,  425 

of  fuels,  419 
Cannizzaro's    Theory    of    Atomic 

Equivalency,  43 
Carnot's  Cycle,  284 

application  of,  to  solutions,  287 
Catalysis,  458,  498 
Catalysts,  498 


542 


INDEX 


Catalysts,  metallic,  502 
Catalytic  agent,  498 

processes,  501 
Catalyzer,  458 
Cataphoresis,  452 
Cell  constant,  315 
Charles'  or  Gay  Lussac's  Law,  20 

deduction  of,  from  the  Kinetic 

Theory  of  Gases,  83 
Chemical  affinity,  476 
Chemical  compound,  definition  of, 

9,  151 

Chemical  formula,  definition  of,  14 
Clausius'  equation,  100 
Clausius'  theory,  307 
Coagulation,  448 

by  electrolytes,  449 
Colligative    properties,    322,    371, 

402 

Colloidality,  442 
Colloid  chemistry,  443,  445 

applications  of,  468 
Colloids,  255,  435 

general  character  of,  437 
Colloid  solutions,  colligative  prop- 
erties of,  460 

osmotic  pressure  of,  461 

physical  properties  of,  459 
Colloid  state,  440,  444 
"Colloid    systems,    preparation    of, 

473 

by  condensation,  473 
by  dispersion,  473,  474 
Components,  definition  of,  148 
Concentrated  solutions,  358 
Conductance,    effect    of    tempera- 
ture on,  330 
Conductors,    electrical   classes   of, 

301 

Conjugate  points,  165 
Consolute  liquids,  157 
Constant  boiling  mixture,  178 
Contact  poisons,  503 
Cooling    curves,    construction    of, 

207,  245 
types  of,  231-233 


Copper  sulphate- water  system,  226 
Corresponding  states,  in 

law  of,  109 
Critical  constants,   calculation  of, 

104 

Critical  pressure,  definition  of,  171 
Critical     solubility,     temperature, 

159 

Critical  temperature,  definition  of, 

171 

Critical  thermal  points,  251 
Cryohydrate,  209 
Cryohydric  point,  209 

temperature,  209 
Crystalloids,  255,  435 

Dalton's  absorption  law,  155 
Dalton's  Law,  60 
Deacon  process,  501 
Degree  of  reaction,  485 
Deliquescence,  228 
Density,  definition  of,  5 

relations  of  gases,  30 
Deviation  from  Charles'  Law,  49 
Dialysis,  255,  436 
Dielectric  constant,  399 

table  of,  400 
Diffusion,  433 
Diffusion  of  gases,  87 
Dilution  Law,  Bancroft's,  331 

Ostwald's,  337 

Rudolphi's,  338 

van't  Hoff's,  339 
Disperse  means,  441 

phase,  441 

system,  441 

Dispersion,  degree  of,  441 
Dispersivity,  132 
Dispersoids,  441 

classification  of,  442 
Dissociation  constant,  58,  337,  340 

degree  of,  54 

of  gases,  52,  60 

of  water,  387 

Distribution  Law,  Nernst's,  166 
Doebereiner's  triads,  66 


INDEX 


543 


Dualistic  theory,  302 

Dulong  and  Petit 's  Law,  413 

Dumas'  method,  31 

Dynamic  allotropy,   definition  of, 

192 
Dyne,  definition  of,  4 

Efflorescence,  228 
Effusion,  Graham's  Law  of,  88 
Electrical  conductance,  301 
Electrochemical    theory,     Davy's, 

301 

Electrolysis,  definition  of,  305 
Electrolytes,  classification  of,  328 

definition  of,  305 
Electrolytic  dissociation,  321 

degree  of,  325 

table  of,  326 

theory,  323 
Electromagnetic    rotatory    power, 

142 

Element,  definition  of,  8 
Emulsoids,  446 
Enantiotropic  substances,  190 

table  of,  191 
Endosmose,  452 
Endosmosis,  255 
Endothermic  reactions,  418 
Energy,  availability  of,  283 
Enzymes,  458 
Equation  of  state,  18 

the  reduced,  108 
Equilibrium  constant,  58 

labile,  187 

of    an    electrolyte   in    solution, 

337 
Equivalent  conductance,  314 

of  inorganic  salts,  table  of,  316 

method  of  calculation,  329 
Equivalent     ionic     conductances, 

table  of,  320 
Eutectic,  209 

point,  209 

table  of,  213 

temperature,  209 
Exosmosis,  255 


Exothermic  reactions,  418 
Explosion,  time  of,  497 

Faraday,  a,  308,  323 

Faraday's  Law,  304 

Ferric  chloride-water  system,  224 

Flash  point,  495 

Force,  definition  of,  4 

unit  of,  4 

Formula  volume,  16 
Formula  weight,  14,  32 
Fractional  crystallization,  238 
Fractional  distillation,  177 

with  steam,  181 
Freezing  curve,  209 
Freezing  mixtures,  properties,  214 
Freezing  point  constant,  299 
equation,  297 

'gram-molecular  lowering  of,  294 
of  concentrated  solutions,  373 
of  solutions,  273 
table  of,  296 

Freezing    point    curves,    Type    I, 
intermediate,  236 
maximum,  236 
minimum,  237 
Type  II,  show  transition  point, 

238 

show  eutectic  point,  241 
show  chemical  compound,  243 
Friedel  and  Craft's  reaction,  501 
Froth,  production  of  a,  471 
Fusibility  curves  of  binary  alloys, 

231 
Fusion  point,  204 

Gas,  as  solvent,  152 

as  solute,  153 
Gas  Law,  the,  18 

constant  of,  24 

deduction  of,  from  the  Kinetic 

Theory  of  Gases,  82 
Gas  law  equation,  application  of, 
to  osmotic  pressure,  261 

development  of,  21 
Gel,  444 


544 


INDEX 


Gladstone- Dale  formula,  125 
Graham's  Effusion  Law,  88 
Gram-molecular  volume,  26,  29 
Gram-molecular  weight,  25 
Gravitational  units,  4 
Grotthus'  Theory,  305 

Heat  capacity,  definition  of,  90 
Heat  of  combustion,  416,  418 

dilution,  416,  418,  427 

relation  to  osmotic   pressure, 
366 

dissociation,  431 

formation,  416,  418 

fusion,  418 

hydration,  428 

ionization,  416,  431 

neutralization,  416,  429 

precipitation,     198,     416,     427, 
429 

reaction,  416 

solution,  416,  427 

vaporization,  416 
Henry's  Law,  statement  of,  153 

exceptions  to,  154 
Hess'  Law  of  Constant  Heat  Sum- 
mation, 417 

Hydrate  theory  of  solutions,  368 
Hydration  of  ions,  380, 383 
Hydrogenation  of  oils,  503 

mechanism  of,  504 
Hydrolysis,  degree  of,  391 

table  of,  393 
Hydrolytic  constant,  389 

Ignition  temperature,  495 
Index  of  refraction,  123 
Inversion  of  cane  sugar,  by  acids, 
489 

by  salts,  490 
Ionic  product,  350 

definition  of,  351 

of  water,  387 

table  of,  353 
Ions,  323 

definition  of,  304 

neutral  effect  of,  347 


Ionization  constant,  table  of,  341 
Isocolloids,  445 
Isohydric  solutions,  343 

definition  of,  347 
Isomorphous  mixtures,  229 
Isothermal,  definition  of,  284 
Isotonic  solutions,  264 
Isotropes,  9 

Kindling  temperature,  495 
Kinetic  Theory  of  Gases,  82 

deduction  of  the  Gas  Law  from, 

82 
Kohlrausch's  Law,  313,  318 

Law,  definition  of,  6 

Law  of  combination  by  volume,  15, 

39 

definition  proportions,  6,  8 
mass  action,  56,  478 

thermodynamic  deduction  of, 
480 

mixtures,  369 
octaves,  69 

Linder-Picton-Hardy  Law,  450 
Liquids,  physical  properties  of,  in 
Liquidus  curve,  234 
Lorentz-Lorenz  formula,  125 
Lyophilic  colloids,  446 
Lyophobic  colloids,  446 

Mass  action,  law  of,  478 

Mass,  units  of,  3 

Mass  Law  equation,  58 

Matter,  3 

Maximum   boiling   point   of   mix- 
tures, table  of,  1 80 

Melting  point,  congruent,  222 

Meso  form,  138 

Minimum  boiling  point  of  mixtures, 
table  of,  1 80 

Mixed  crystals,  229 

Mole,  definition  of,  25 

Molecular  conductance,  315 

Molecular  formulae,  32,  33 

Molecular  heat,  415 
definition  of,  90 


INDEX 


545 


Molecular  theory,  the,  43 

velocity,  86 

volume,  in 

weight,  determination  of,  29 
by  freezing  point  method,  277 
by  boiling  point  method,  279 
Monomolecular  reactions,  482,  487 
Monotropic  substances,  191 
Monotropy,  definition  of,  192 
Motion,  definition  of,  2 
Multiple  proportions,  law  of,  8,  10 
Muta-rotation,  141 

Nicols  prism,  134 

Nonaqueous    solutions,    electrical 

conductance  of,  396 
theories  of,  406 
Nonmiscible  liquids,  157 
Number   of    degrees    of   freedom, 

definition  of,  184 

Optical  rotation,  133 

effect  of  temperature  on^  139 
of  concentration,  140 
of  solvent,  141 
measurement  of,  134 
molecular,  135 
specific,  135 
Ore  flotation,  469 
Osmosis,  definition  of,  255 

mechanism  of,  256 
Osmotic    phenomena,    nature    of, 

462 
Osmotic  pressure,  255 

application    of     the    Gas    Law 

Equation  to,  261 
factors  affecting,  463 
of  colloid  solutions,  461 
of  concentrated  solutions,  365 
of  solutions,  262 

relation  of,  to  concentration,  258 
to  boiling  point,  299 
to  freezing  point,  292 
to  temperature,  260 
to  vapor  pressure,  290,  291 
Ostwald's  Dilution  Law,  337 


Oxidation    and    reduction,    defini- 
tions of,  333 

Parke's  process,  165 
Partially  miscible  liquids,  157 
Peptization,  444 
Perfect  solutions,  358 
Periodic  Law,  the,  69 
Periodic  Systems,  the,  64 

advantages  of,  77 

imperfections  of ,  78 
Periodic  table,  the,  68 

discussion  of,  71 

graphic  representation  of,  80 
Pfeffer's  osmotic  cell,   description 

of,  259 

Phase,  definition  of,  146 
Phase  rule,  applications  of,  248,  253 

definition  of,  185 
Phases,  conception  of,  185 

separation  of,  150 
Plasmolysis,  263 
Polarimeter,  135 
Polarized  light,  133 
Polymorphism,  definition  of,  189 
Poundal,  definition  of,  4 
Precipitation  membranes,  258 
Pressure,  definition  of,  5 
Promoters,  502 
Protective  colloids,  458 
Prout's  hypothesis,  64 
Pseudo-osmotic  pressure,  464 

Quadruple  point,  206 

Racemic  mixtures,  138 

Raoult's  Law,  266 

Reciprocal  Proportions,  Law  of,  10, 

ii 

Reduced  temperatures,  in,  120 
Refraction,  double,  133 

of  light,  122 

Refractive  power,  methods  of  ex- 
pressing, 125 
Refractivity,  specific,  125 

molecular,  126 


546 


INDEX 


Refractivities,  table  of,   127 

of  isomeric  substances,  128 

Refractometers,  kinds  of,  131 

Saponification  of  esters,  492 
Saturated  solutions,  definition   of, 

195 

Shaking  out  process,  166 

Snell's  Law,  123 

Sodium  chloride- water  system,  204 

Sodium  sulphate- water  system,  216 

temperature  concentration  dia- 
gram, 2 17 

pressure    temperature    diagram, 

219 

Sol,  443 
Solid  solutions,  229 

definition  of,  151 
Solidification  curve,  209 
Solidus  curve,  234 
Solubility  curve,  195,  219 

of  hydrates,  220,  221 

of  SO3,  369 

of  water-ether-alcohol  on  a  tri- 
angular diagram,  163 

pitch  of,  197 

types  of,  1 60 
Solubility  product,  351 
Solubility,  relation  of,  to  chemical 

character,  196 
Solute,  definition  of,  151 
Solution,  definition  of,  151 
Solutions,  146,  440 

of  solids  and  liquids,  229 

types  of,  204 
Solvent,  definition  of,  151 
Specific  conductance,  314 
Specific  gas  constant,  25 
Specific  gravity,  definition  of,  5 
Specific  heats,  at  constant  volume, 

9i 

at  constant  pressure,  91 
difference  of,  93 
methods  of  determining,  95 
of  compounds,  415 
of  elements,  413 


Specific  heats —  Cont. 

of  gases,  90 

of  water,  table  of,  91 

ratio  of,  95 
Specific  surface,  441 
Speed,  definition  of,  2 
Stere,  114 

Stoke 's  law  of  moving  particles,  467 
Sublimation  curve,  172 

definition  of,  172 
Sulphur,  system  of,  193 
Sulphur  trioxide- water  system,  224 
Sulphuric  acid,  contact  process,  505 
Surface  tension  of  liquids,  115 

Ramsay  and  Shield's  work  on,  1 16 
Suspensoids,  446 
Symbol  weight,  14 

determination  of,  29,  33 

or  atomic  weight,  34 
System,  definition  of,  146 
Systems,  divariant,  186 

mono  variant,  186 

non  variant,  187 

Tate's  Law,  119 
Temperature  of  explosion,  495 
Theorem  of  Le  Chatelier,  199 

geological  application  of,  201 
Theory,  conception  of,  36,  37 
Thermal  neutrality  of  salt  solutions, 

law  of ,  429 
Thermochemistry,  410 

first  law  of,  417 
Thermodynamic  deduction  of  law 

of  mass  action,  480 
Thermodynamic  equations  for  con- 
centrated solutions,  360 
Thermodynamics , 

first  law  of,  282 

second  law  of,  283 
Thomson's  hypothetic  curve,  102 
Tie  line,  164 
Torricelli's  Law,  88 
Transference  numbers,  308 

table  of,  312 
Transition  point,  definition  of,  190 


INDEX 


547 


Triangular  diagram,  161 
Trimolecular  reactions,  485 
Triple  point,  definition  of,  187 
Trouton's  Law,  120 
Tyndall  effect,  439 

Ultramicroscope,  the,  439 
Unit,  definition  of,  I 
Units,  fundamental,  2 

derived,  2 

gravitational,  4 

of  chemistry,  12 

of  force,  4 

of  mass,  3 
Universal  gas  constant,  25 

numerical  values  of,  26 

Van  der  Waals'  equation,  97 

application  of,  100 
Vapor  composition  curve,  177 
Vapor  pressure  curve,  169 

limits  of,  171 

types  of,  173,  174 
Vapor     pressure,      definition 
1 68 

lowering  of,  265 

lowering  of,   in    relation    to 
motic  pressure,  290 


of, 


os- 


Vapor  pressure  —  Cont. 

of  concentrated  solutions,  376 

of  hydrates,  224 

of  ice,  table  of,  173 

of  water,  table  of,  170 

relation  to  osmotic  pressure,  270 
Vectoriality,  447 
Velocity,  definition  of,  3 
Velocity  of  reactions,  factors  which 

influence,  495 
Victor  Meyer's  method  of  vapor 

density  determinations,  32 
Volume  normality,  359 

Water,  as  catalyst,  500 

constitution  of,  383 

dissociation  of,  386 

ionic  product  of,  387 

system  of,  186 
Water-aniline  system,  159 
Water-ether  system,  185 
Weight,  normality,  359 

definition  of,  4 
Working  hypothesis,  36 
Wiillner's  Law,  266 

Zone  of  anamorphism,  201 
Zone  of  katamorphism,  201 


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